BUS STATS II - Chapter Ten Practice Quiz
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 11 7.26 8 6.74 11 12.85 8 7.28 12 8.12 13 9 5 6.26 4 5.51 11 8.13 6 6.43 6 5.89
Create a scatterplot of the data. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] y-hat = 3.69 + 0.452x [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. [] Identify a characteristic of the data that is ignored by the regression line. There is an influential point that strongly affects the graph of the regression line.
Twenty different statistics students are randomly selected. For each of them, their body temperature (°C) is measured and their head circumference (cm) is measured. If it is found that r = 0, does that indicate that there is no association between these two variables?
No, because while there is no linear correlation, there may be a relationship that is not linear.
Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x-bar=97, y-bar=98.8, r=0.893, P-value=0.000, and y-hat = 20.25+0.81x, where x represents the IQ score of the younger child. Find the best predicted value of y-hat given that the younger child has an IQ of 108? Use a significance level of 0.05.
The best predicted value of y-hat is 107.73. [Using the formula given fill x with 108: 20.25+0.81(108) = 107.73].
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). If only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why?
The best variable is _HWY_ because it has the best combination of _small_ P-value, _0_, and _large_ adjusted R^2, _0.920_.
The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 26.3 cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 26.3 cm, what is the single value that is the best predicted height for that person?
The single value that is the best predicted height is 181 cm. [Using the display given, find the "New Obs" portion and under "Fit" round appropriately for the answer].
Using the lengths (in.), chest sizes (in.), and weights (lb) of bears from a data set, the resulting regression equation is Weight = -274 + 0.426 Length + 12.1 Chest Size. The P-value is 0.000 and the adjusted R^2 value is 0.925. If an additional predictor variable of neck size (in.) is included, the P-value becomes 0.000 and the adjusted R^2 becomes 0.933. Why is it better to use values of adjusted R^2 instead of simply using values of R^2?
The unadjusted R^2 increases or remains the same as more variables are included, but the adjusted R^2 is adjusted for the number of variables and sample size.
Refer to the data table below. Complete parts (a) through (d). IQ, Brain Volume, Weight Data: IQ Brain_Volume_(cm3) Body_Weight_(kg) 95 1007 57.898 90 962 58.894 88 1033 64.727 87 1028 58.145 102 1281 63.602 102 1271 61.561 102 1051 133.076 95 1081 107.138 126 1036 62.371 125 1072 82.951 100 1174 61.437 95 1079 61.563 94 1069 84.966 87 1105 79.565 95 1344 97.344 85 1440 99.202 98 1030
[Copy Data into Statcrunch, Stat, Regression, MULTIPLE Linear, Y Variable is the item being solved for [IQ], Alternate Choosing the following for the x Variable [W then VOL then W and VOL] to find which one has the largest "R-squared (adjusted)" and smallest "P-value"] [] a. Find the best regression equation with IQ score as the response variable. Use predictor variables of brain volume (VOL) and/or weight (W). Select the correct choice and fill in the answer boxes to complete your choice. [Because VOL had the largest "R-squared (adjusted)" and smallest "P-value", use the formula under "Multiple linear regression results" to fill in the blanks on MyMathLab] ***Another important thing to know about negative numbers is that they get smaller the farther they get from 0. On this number line, the farther left a number is, the smaller it is. So 1 is smaller than 3. -2 is smaller than 1, and -7 is smaller than -2.*** IQ = 108.1531+ (-0.0065) VOL [] Why is this equation best? It is the best equation of the three because it has the highest adjusted R^2, the lowest P-value, and the fewest number of predictor variables. [] c. Based on these results, can a researcher predict someone's IQ score if he or she knows the volume and weight of their brain? No, because the adjusted R^2 value is low. Predictions using the regression equation are unlikely to be accurate. [] d. Based on these results, does it appear that people with larger brains have higher IQ scores? No, because the regression equation does not have overall significance.
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). Which regression equation is best for predicting city fuel consumption? Why?
[] Choose the correct answer below. The equation CITY = -3.16 + 0.817HWY is best because it has a low P-value and its R^2 and adjusted R^2 values are comparable to the R^2 and adjusted R^2 values of equations with more predictor variables.
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it best? Is the best regression equation a good regression equation for predicting the nicotine content? Why or why not? Cigarette Content Data: Tar Nicotine CO 5 0.5 5 15 1.0 18 18 1.3 17 13 0.7 18 12 0.8 18 13 1.0 12 14 1.1 17 14 1.1 15 16 1.0 16 9 0.8 12 13 0.7 17 14 0.8 17 14 0.9 18 15 0.9 17 1 0.3 4 15 1.1 19 15 1.0 16 13 0.7 17 14 1.0 16 15 0.9 18 15 1.1 15 15 1.0 16 7 0.7 8 17 1.2 17 15 1.1 14
[Copy Data into Statcrunch, Stat, Regression, MULTIPLE Linear, Y Variable is the item being solved for [Nicotine], Alternate Choosing the following for the x Variable [Tar then CO then Tar and CO] to find which one has the largest "R-squared (adjusted)" and smallest "P-value"] [] Find the best regression equation for predicting the amount of nicotine in a cigarette. Use predictor variables of tar and/or carbon monoxide (CO). Select the correct choice and fill in the answer boxes to complete your choice. [Because Tar+CO had the largest "R-squared (adjusted)" and smallest "P-value", use the formula under "Multiple linear regression results" to fill in the blanks on MyMathLab] Nicotine = 0.344 + (0.082) Tar + (-0.034) CO [] Why is this equation best? It is the best equation of the three because it has the highest adjusted R^2, the lowest P-value, and removing either predictor noticeably decreases the quality of the model. [] Is the best regression equation a good regression equation for predicting the nicotine content? Why or why not? Yes, the small P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.
The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126. Redshift Distance 0.0232 0.34 0.0538 0.77 0.0716 0.99 0.0393 0.56 0.0442 0.61 0.0107 0.13
[Copy Data into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Under "Perform" Click Confidence Intervals and adjust for 0.90, under "Prediction of Y" adjust "X value(s)" to 0.0126 and "Level" to 0.90, Compute:] [] a. Find the explained variation. 0.463307 *** On Statcrunch: Explained variation is the intersection of "Model" and "SS". [] b. Find the unexplained variation. 0.001226 ***On Statcrunch: The Unexplained variation is the intersection of "Error" and "SS". [] c. Find the indicated prediction interval. 0.129 billion light-years < y < 0.221 billion light-years [ On Statcrunch scroll to "Predicted Values" and under "90% P.I. for new" is the answers].
The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with a diamond that weighs 0.8 carats. Weight Price 0.3 500 0.4 1150 0.5 1341 0.5 1415 1.0 5664 0.7 2269
[Copy Data into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Under "Perform" Click Confidence Intervals and adjust for 0.95, under "Prediction of Y" adjust "X value(s)" to 0.8 and "Level" to 0.95, Compute:] [] a. Find the explained variation. 16131074 *** On Statcrunch: Explained variation is the intersection of "Model" and "SS". [] b. Find the unexplained variation. 1096035 ***On Statcrunch: The Unexplained variation is the intersection of "Error" and "SS". [] c. Find the indicated prediction interval. $2048 < y < $5413 [ On Statcrunch scroll to "Predicted Values" and under "95% P.I. for new" is the answers].
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude Temperature 4 60 6 38 13 28 24 -3 27 -33 31 -41 32 -60
[Copy Data into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Under "Perform" Click Confidence Intervals and adjust for 0.95, under "Prediction of Y" adjust "X value(s)" to 6.327 and "Level" to 0.95, Compute:] [] a. Find the explained variation. 11632.53 *** On Statcrunch: Explained variation is the intersection of "Model" and "SS". [] b. Find the unexplained variation. 557.19 ***On Statcrunch: The Unexplained variation is the intersection of "Error" and "SS". [] c. Find the indicated prediction interval. 16.4408 degrees F < y < 79.5991 degrees F [ On Statcrunch scroll to "Predicted Values" and under "95% P.I. for new" is the answers].
Listed below are amounts of court income and salaries paid to the town justices for a certain town. All amounts are in thousands of dollars. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 99% confidence level with a court income of $800,000 Court_Income Justice_Salary 65 28 396 43 1574 97 1101 57 260 42 252 57 104 23 152 22 35 19
[Copy Data into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Under "Perform" Click Confidence Intervals and adjust for 0.99, under "Prediction of Y" adjust "X value(s)" to 800 and "Level" to 0.99, Compute:] [] a. Find the explained variation. 4032.042 *** On Statcrunch: Explained variation is the intersection of "Model" and "SS". [] b. Find the unexplained variation. 918.847 ***On Statcrunch: The Unexplained variation is the intersection of "Error" and "SS". [] c. Find the indicated prediction interval. $14.9673 < y < $101.6427 [ On Statcrunch scroll to "Predicted Values" and under "99% P.I. for new" is the answers].
When using the numbers of points scored in each Super Bowl from 1980 to the last Super Bowl at the time that this exercise was written, we obtain the following values of R^2 for the different models: linear: 0.002; quadratic: 0.082; logarithmic: 0.003; exponential: 0.005; power: 0.001. Based on these results, which model is best? Is the best model a good model?
[] Choose the correct answer below. Quadratic is best, but it is not a good model.
Listed below are the annual high values, y, of a stock market index for each year beginning with 1990. Let x represent the year, with 1990 coded as x=1, 1991 coded as x=2, and so on. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the best model to predict the annual high value of the stock market index for the year 2010. Is the predicted value close to the actual value of 11,655? x_(year) y_(stock_market_index) 1990 3042 1991 3105 1992 3361 1993 3819 1994 4044 1995 5220 1996 6591 1997 8220 1998 9326 1999 11618
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the best model? Choose the correct answer below and fill in the answer boxes within your choice. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch make a new column [var3] where you subtract the according year to the first year [1975] adding one to the result each time ending up with [1-10] and chose "var3" for X and "y_(stock_market_index)" for Y columns, Stat, Regression, Polynomial, Transformation window has no changes but make sure "Poly. Oder" is set at 2, under "Parameter Estimates" section use the "Estimate" column for results to fill in the blanks]. y = ax^2 + (b)x + (c) -> [QUADRATIC FORMULA] y = 124.830x^2 + (-436.652)x + (3430.25) [] Use the best model to predict the annual high value of the stock market index for the year 2010. Is the predicted value close to the actual value of 11,655? Select the correct choice below and fill in the answer box to complete your choice. [First find the x value by doing (2010-1990)+1 = 21, Then using the previous answer, fill in the equation with x=22: 124.830(21)^2 + (-436.652)(21) + (3430.25) 49311 Then select and fill blank: No, the predicted value of _49311_ for the year 2010 is dramatically greater than the actual value of 11,655.
In a carefully controlled experiment, bacteria are allowed to grow for a week. The number of bacteria are recorded at the end of each day, as shown below. Construct a scatterplot and identify the mathematical model that best fits the given data. x_(day) y_(number_of_bacteria) 1 21 2 42 3 77 4 142 5 331 6 599 7 1391
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch choose proper X and Y columns, Stat, Regression, Simple Linear, Transformation Window "X:None" but "y:log(y)", under "Parameter Estimates" section use the "Estimate" column for results, BUT transform intercept in results window with {on TI-84} [a=] e^intercept AND transform slope in results window with {on TI-84} [b=] e^slope.] y = (a) b^x [EXPONENTIAL FORMULA] [y-intercept result: 2.3091026 e^intercept: 10.0653879217] slope result: 0.69118801 e^slope: 1.99608549472] y = (10.065) 1.996^x
Listed below are the amounts (in millions of dollars) grossed during the first three weeks of a new movie. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the model to predict the gross amount on the 22nd day of the movie's release. Is the result close to the actual amount of $2.2 million? Is there any characteristic of the data not revealed by the model? Days Gross_Amounts_(millions of dollars) 1 57.9 2 22.2 3 27 4 29.5 5 21.8 6 9.6 7 9.4 8 7.9 9 6.9 10 9.4 11 11.2 12 8.9 13 4.4 14 4.4 15 4.5 16 3.9 17 5.7 18 6.9 19
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch choose proper X and Y columns, Stat, Regression, Simple Linear, Transformation Window "X:log(x)" but "y:log(y)", under "Parameter Estimates" section use the "Estimate" column for results, BUT transform intercept in results window with {on TI-84} [a=] e^intercept BUT keep the slope the same.] y = (a)x ^b ->[POWER FORMULA] [y-intercept result: 4.1869737 e^intercept: 65.823288218] slope result: -0.94057799] y = (65.823)x ^(-0.941) [] Use the model to predict the gross amount on the 22nd (x=22) day of the movie's release. The predicted gross amount on day 22 is [Using the previous formula substitute x for 22: (65.823)(22) ^(-0.941)=] 3.6 [] Is the result close to the actual amount of $2.2 million? No, the result is not very close to the actual amount. The prediction overestimates the gross amount on day 22. [] Is there any characteristic of the data not revealed by the model? (Hint: The movie opened on a Wednesday.) Yes, the model does not take into account the fact that movies do better on weekend days.
The table below lists different amounts (metric tons) of explosives and the corresponding value on the Richter scale for the explosions. Construct a scatterplot and identify the mathematical model that best fits the given data. x_(metric_tons) y_(Richter_scale) 2 3.2 11 3.9 15 4.1 55 4.3 81 4.7 548 5.1
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch choose proper X and y columns, Stat, Regression, Simple Linear, Transformation window "X:log(x)" and "Y:None", under "Parameter Estimates" section use the "Estimate" column for results to fill in the blanks]. y = a + b(ln x) -> [LOGARITHMIC FORMULA} y = 3.069 + 0.336(ln x)
An experiment involves dropping a ball and recording the distance it falls (y) for different times (x) after it was released. Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models. Time_(seconds) Distance_(meters) 0.5 1.2 1 4.8 1.5 10.6 2 18.3 2.5 27.7 3 38.4
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch chose proper X and Y columns, Stat, Regression, Polynomial, Change nothing in the Transformation window but make sure "Poly. Order:" is at 2, under "Parameter Estimates" section use the "Estimate" column to fill in the answer"] y = ax^2 + (b)x + (c) -> [QUADRATIC FORMULA] y = 3.564x^2 + (2.519)x + (-1.09)
The table shown below lists the cost y (in dollars) of purchasing cubic yards of red landscaping mulch. The variable x is the length (ft) of each side of a cubic yard. Construct a scatterplot and identify the mathematical model that best fits the given data. x_(ft) y_(dollars) 1 5.2 2 9.9 3 14.6 4 19.3 5 24 6 28.7
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch chose proper X and Y columns, Stat, Regression, Simple Linear, under "Parameter Estimates" section use the "Estimate" column to fill in the answer"] y = a + bx [LINEAR FORMULA] y = 0.5 + 4.7x
Construct a scatterplot and identify the mathematical model that best fits the data shown below. Let x represent the year since 1959, with 1960 coded as x=1, 1973 coded as x=14,1986 coded as x=27, and so on. Let y represent the subway fare. Year Subway_Fare 1960 0.20 1973 0.40 1986 0.90 1995 1.30 2002 1.55 2003 1.95
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch make a new column [var3] where you subtract the according year to the first year [1960] adding one to the result each time ending up with [1, 14, 27, 36, 43, 44] and chose "var3" for X and "Subway_Fare" for Y columns, Stat, Regression, Simple Linear, Transformation Window "X:None" but "y:log(y)", under "Parameter Estimates" section use the "Estimate" column for results, BUT transform intercept in results window with {on TI-84} [a=] e^intercept AND transform slope in results window with {on TI-84} [b=] e^slope.] y = (a) b^x [EXPONENTIAL FORMULA] [y-intercept result: -1.6161297 e^intercept: 0.19866611051] slope result: 0.051115986 e^slope: 1.05244495508] y = (0.199) 1.052^x
Listed below are the numbers of deaths resulting from motor vehicle crashes. Let x represent the year, with 1975 coded as x=1, 1980 coded as x=6, 1985 coded a x=11, and so on. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the best model to find the projected number of deaths for the year 2022. x_(year) y_(deaths) 1975 44527 1980 51104 1985 43802 1990 44588 1995 41820 2000 41968 2005 43455 2010 32679
[] Choose the correct scatterplot below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. [With Data in Statcrunch make a new column [var3] where you subtract the according year to the first year [1975] adding one to the result each time ending up with [1, 6, 11, 16, 21, 26, 31, 36] and chose "var3" for X and "y(deaths)" for Y columns, Stat, Regression, Polynomial, Transformation window has no changes but make sure "Poly. Oder" is set at 2, under "Parameter Estimates" section use the "Estimate" column for results to fill in the blanks]. y = ax^2 + (b)x + (c) -> [QUADRATIC FORMULA] y = -12.940x^2 + (170.572)x + (45964.493) [] Use the best model to find the projected number of such deaths for the year 2022. [First find the x value by doing (2022-1975)+1 = 48, Then using the previous answer, fill in the equation with x=48: -12.940(48)^2 + (170.572)(48) + (45964.493) =] The projected number of deaths in year 2022 is _24338_
Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. The accompanying table lists the heights (cm) from several recent presidential elections. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of a = 0.01. President (cm) Opponent (cm) 182 178 179 176 189 185 179 178 180 182 180 178 194 181 182 175 176 178 179 179 187 174 183 188 188 189 185 171
[] Construct a scatterplot. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] The linear correlation coefficient is r = 0.282. [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] Determine the null and alternative hypotheses. H0: p = 0 H1: p ≠ 0 [] The test statistic is t = 1.02. [Within the same popup that gave you the r value, look under "Parameter estimates" for the T-Stat in the Slope row]. [] The P-value is 0.329. [Within the same popup that gave you the r value, look under "Parameter estimates" for the P-value in the Slope row]. [] Because the P-value of the linear correlation coefficient is _greater_ than the significance level, there _is not_ sufficient evidence to support the claim that there is a linear correlation between the heights of winning presidential candiates and the heights of their opponents. [] Should we expect that there would be a correlation? No, because presidential candidates are nominated for reasons other than height.
A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. Correlation matrix: Variables: Paper Glass Paper 1 0.1226 Glass 0.1226 1
[] Determine the null and alternative hypotheses. H0: p = 0 H1: p ≠ 0 [] Identify the correlation coefficient, r. r = .123 [Round the decimal in the table to three decimal places]. [] Identify the critical value(s). There are two critical values at r = ± .254 [Use the given table of critical values link to find the critical value at 0.05 for 60]. [] State the conclusion. Because the absolute value of the correlation coefficient is _less than or equal to_ the positive critical value, there _is not_ sufficient evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α=0.05
Use the accompanying paired data consisting of registered boats (tens of thousands) and manatee fatalities from boat encounters. Let x represent the number of registered boats and let y represent the corresponding number of manatee deaths. Use the given number of registered boats and the given confidence level to construct a prediction interval estimate of manatee deaths. Use xequals81 (for 810,000 registered boats) with a 99% confidence level.
[] Find the indicated prediction interval. 37208 manatees < y < 91701 manatees [Copy Data into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Under "Perform" Click Confidence Intervals and adjust for 0.99, under "Prediction of Y" adjust "X value(s)" to 81 and "Level" to 0.99, Compute, Scroll to "Predicted Values" and under "99% P.I. for new" is the answers].
The accompanying table provides data for the sex, age, and weight of bears. For sex, let 0 represent female and let 1 represent male. Letting the response (y) variable represent weight, use the dummy variable of sex and the variable of age and to find the multiple regression equation. Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear? a. Female bear that is 18 months of age b. Male bear that is 18 months of age
[] Find the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables. [Copy Data into Statcrunch, Stat, Regression, MULTIPLE Linear, Y Variable is the item being solved for [Weight], Choose Sex and Age for X Variable, use the formula under "Multiple linear regression results" to fill in the blanks on MyMathLab] Weight = _2.4_ + (_83.9_) Sex + (_2.9_) Age [] Predict the weight of a female bear that is 18 months of age. [Using the equation from the previous answer, fill in 0 for Sex and 18 for Age: 2.4 + 83.9 (0) + 2.9 (18) =] 55 [] Predict the weight of a male bear that is 18 months of age. [Using the equation from the previous answer, fill in 1 for Sex and 18 for Age: 2.4 + 83.9 (1) + 2.9 (18) =] 139 [] Does sex appear to have much of an effect on the weight of a bear? Select the correct choice and fill in the answer box to complete your choice. [Using the exact answers from the previous two questions, subtract to find the difference: 138.5-54.6=83.9] Yes, the sex of a bear does appear to have an effect on its weight. The regression equation indicates that the predicted weight of a male bear is about _83.9_ pounds more than a female bear of the same age.
Using the lengths (in.), chest sizes (in.), and weights (lb) of bears from a data set, a researcher gets the regression equation below. Weight = -274 + 0.426 Length + 12.1 Chest Size Identify the response and predictor variables in this regression equation.
[] Select the correct response. The response variable is weight and the predictor variables are length and chest size.
If the coefficient beta-1 has a nonzero value, then it is helpful in predicting the value of the response variable. If beta-1 = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that beta-1 = 0 use the test statistic t = (b1 - 0) / sb. Critical values or P-values can be found using the t distribution with n - (k + 1) degrees of freedom, where k is the number of predictor (x) variables and n is the number of observations in the sample. The standard error sb1 is often provided by software. For example, see the accompanying technology display, which shows that sb1 = 0.074268936 (found in the column with the heading of "Std. Err." and the row corresponding to the first predictor variable of height). Use the technology display to test the claim that beta-1 = 0. Also test the claim that beta-2 = 0. What d
[] Test the claim that beta-1 = 0. [Using the given table fill in the blanks with the provided information, using the "Height" row to complete the first question, where the regression coefficient b1 is under the "Estimate" column] For H0: _beta-1 = 0_, the test statistic is t = _9.955_ and the P-value is _0_, so _reject_ H0 conclude that the regression coefficient b1 = _0.739_ should _be_ kept. [] Test the claim that beta-2 = 0. [Using the given table fill in the blanks with the provided information, using the "Waist" row to complete the first question, where the regression coefficient b2 is under the "Estimate" column] For H0: _beta-2 = 0_, the test statistic is t = _29.440_ and the P-value is _0_, so _reject_ H0 conclude that the regression coefficient b2 = _1.008_ should _be_ kept. [] What do the results imply about the regression equation? The results imply that the regression equation should include both independent variables of height and waist as both are useful in predicting the response variable.
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). The equation CITY = -3.13 + 0.823HWY was previously determined to be the best for predicting city fuel consumption. A car weighs 2700 lb, it has an engine displacement of 2.3 L, and its highway fuel consumption is 37 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?
[] The best predicted value of the city fuel consumption is 27.321, mi/gal [Using the provided equation, replace HWY with 37: -3.13+0.823(37) = 27.321 The predicted value _is_ likely to be a good estimate and _is not_ likely to be very accurate because _the sample consists of only 21 cars_.
Assume that you have paired values consisting of heights (in inches) and weights (in lb) from 40 randomly selected men. The linear correlation coefficient r is 0.518. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?
[] The coefficient of determination is 0.268: 26.8% of the variation is explained by the linear correlation, and 73.2% is explained by other factors.
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 27 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 27 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts?
[] The linear correlation coefficient is -.796. [Using the Minitab display given, find "R-Sq", then divide that by 100, then square root that decimal, and then make it negative by adding a "-" sign, and that is your answer]. [] Is there sufficient evidence to support a claim of linear correlation? Yes.
Find the regression equation, letting overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 2 cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05. Overhead_Width_(cm) Weight_(kg) 8.1 174 7.5 179 9.4 255 7.3 138 8.7 220 9.8 273
[] The regression equation is y-hat = -214.9+49.8 [Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. [] The best predicted weight for an overhead width of 2 cm is -115.3 kg. [Using the previous formula, insert 2 in for x: -214.9+49.8(2) = -115.3]. [] Can the prediction be correct? What is wrong with predicting the weight in this case? The prediction cannot be correct because a negative weight does not make sense. The width in this case is beyond the scope of the available sample data.
Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $100 million. Use a significance level of alpha equals 0.05. Budget ($) in Millions Gross ($) in Millions 40 120 22 9 117 108 69 69 72 122 53 117 119 96 68 110 6 47 57 104 121 211 21 30 5 25 150 287 7 56
[] The regression equation is y-hat = 23.2+1.3x. [Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. [] The best predicted gross for a movie with a $100 million budget is $153.2 million. [Using the previous formula, insert 100 in for x: 23.2+1.3(100) = 153.2].
Let the predictor variable x represent heights of males and let response variable y represent weights of males. A sample of 149 heights and weights results in s-subscript-e = 16.85949 cm. In your own words, describe what that value of s-subscript-e represents.
[] The value of s-subscript-e is the standard error of the estimate, which is a measure of the differences between the observed weights and the weights predicted from the regression equation.
Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using α = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? Lemon_Imports_(x) Crash_Fatality_Rate_(y) 228 15.9 265 15.6 357 15.5 480 15.3 531 14.8
[] What are the null and alternative hypotheses? H0: p = 0 H1: p ≠ 0 [] Construct a scatterplot. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] The linear correlation coefficient is r = -0.934 [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] The test statistic is t = -4.543. [Within the same popup that gave you the r value, look under "Parameter estimates" for the T-Stat in the Slope row]. [] The P-value is 0.02. [Within the same popup that gave you the r value, look under "Parameter estimates" for the P-value in the Slope row]. [] Because the P-value is _less_ than the significance level 0.05, there _is_ sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α = 0.05. [] Do the results suggest that imported lemons cause car fatalities? The results do not suggest any cause-effect relationship between the two variables.
Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? Court_Income Justice_Salary 65.0 29 402.0 42 1567.0 90 1132.0 55 273.0 46 252.0 60 112.0 26 153.0 27 30.0 17
[] What are the null and alternative hypotheses? H0: p = 0 H1: p ≠ 0 [] Construct a scatterplot. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] The linear correlation coefficient is r = 0.863 [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] The test statistic is t = 4.519 [Within the same popup that gave you the r value, look under "Parameter estimates" for the T-Stat in the Slope row]. [] The P-value is 0.003. [Within the same popup that gave you the r value, look under "Parameter estimates" for the P-value in the Slope row]. [] Because the P-value is _less_ than the significance level 0.05, there _is_ sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of α = 0.05. [] Based on the results, does it appear that justices might profit by levying larger fines? It does appear that justices might profit by levying larger fines.
The accompanying data are the annual high values of a stock market index in order by row for each year beginning with 1990. Find the best model and then predict the value for the year 2014 (the last year listed). Is the predicted value close to the actual value of 18,093? Let x=1 for the year 1990. 3,048 3,175 3,452 3,810 4,028 5,166 6,512 8,242 9,402 11,598 11,386 11,317 10,588 10,410 10,812 10,900 12,430 14,193 13,343 10,634 11,657 12,918 13,601 16,611 18,093
[] What is the best model? Choose the correct answer below and fill in the answer boxes within your choice. [Copy Data in Statcrunch choosing to place the pasted data into one single column, Make a new column [1-25], Choose X:"Var 2" and Y:"Var 1" columns, Stat, Regression, Simple Linear, Transformation Window "X:log(x)" but "y:log(y)", under "Parameter Estimates" section use the "Estimate" column for results, BUT transform intercept in results window with {on TI-84} [a=] e^intercept BUT keep the slope the same.] y = (a)x ^b ->[POWER FORMULA] [y-intercept result: 7.6623607 e^intercept: 2126.77217817] slope result: 0.61168652] y = (2126.772)x ^(0.612) [] Use this model to predict the value for the year 2014. The model's predicted value is [First find the x value by doing (2014-1990)+1 = 25, Then using the previous answer, fill in the equation with x=25: (2126.772)(25) ^(0.612) =] 15250. [] How does the model's predicted value compare to the actual value of 18,093? The model _underestimates_ the value by _2843_. [Subtract 18093-15250 = 2843].
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 51 inches. Is the result close to the actual weight of 442 pounds? Use a significance level of 0.05. Chest_size_(inches) Weight_ (pounds) 45 352 50 374 43 275 43 314 52 440 52 367
[] What is the regression equation? y-hat = -172.6 + 11.1x [Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. [] What is the best predicted weight of a bear with a chest size of 51 inches? The best predicted weight for a bear with a chest size of 51 inches is 393.5 pounds. [Using the previous formula, insert 51 in for x: -172.6 + 11.1(51) = 393.5]. [] Is the result close to the actual weight of 442 pounds? This result is not very close to the actual weight of the bear.
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min Temperature (°F) 1155 92.7 1135 89.7 1107 90 1056 84.2 766 63.8 942 73
[] What is the regression equation? (Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.) y-hat = 4.08 + 0.0761x [Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. [] What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute? The best predicted temperature when a bug is chirping at 3000 chirps per minute is 232.4 degrees F. [Using the previous formula, insert 51 in for x: 4.08 + 0.0761(3000) = 232.4]. [] What is wrong with this predicted value? Choose the correct answer below. It is unrealistically high. The value 3000 is far outside of the range of observed values.
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.336
[] What is the value of the coefficient of determination? r^2 = .1129 [Square root r value]. [] What is the percentage of the total variation that can be explained by the linear relationship between the two variables? Explained variation = 11.29% [Multiply the r-squared value by 100 to get a percentage].
Use the given data set to complete parts (a) through (c) below. (Use α=0.05.) x y 10 7.47 8 6.76 13 12.74 9 7.11 11 7.82 14 8.83 6 6.08 4 5.39 12 8.14 7 6.42 5 5.72
[] a. Construct a scatterplot. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r = 0.816. [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. There is _sufficient_ evidence to support the claim of a linear correlation between the two variables. [] c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below. The scatterplot reveals a perfect straight-line pattern, except for the presence of one outlier.
Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. b. Find the value of the correlation coefficient r and determine whether there is a linear correlation. c. Remove the point with coordinates (9,1) and find the correlation coefficient r and determine whether there is a linear correlation. d. What do you conclude about the possible effect from a single pair of values?
[] a. Do the data points appear to have a strong linear correlation? Yes. [] b. What is the value of the correlation coefficient for all 10 data points? r = -0.893 [Manually insert the data points into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] Is there a linear correlation between x and y? Use α = 0.01. Yes, because the correlation coefficient is _in_ the critical region. [] What is the correlation coefficient when the point (9, 1) is excluded? r = 0. [Remove the final data set in Statcrunch and follow the same steps: Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] Is there a linear correlation between x and y? Use α = 0.01. No, because the correlation coefficient is _not in_ the critical region. [] d. What do you conclude about the possible effect from a single pair of values? The effect from a single pair of values can change the conclusion.
a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?
[] a. What is a residual? A residual is a value of y-[y-hat], which is the difference between an observed value of y and a predicted value of y. [] b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the _sum of squares_ of the residuals is the _lowest_ possible sum.
Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 125 and a y-intercept of negative 367. Complete parts (a) and (b) below.
[] a. What is the equation of the regression line? Select the correct choice below and fill in the answer boxes to complete your choice. y-hat = -367 + (125) x [] b. What does the symbol y-hat represent? The symbol y-hat represents the predicted value of price.
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 14 19.95 8 16.11 5 9.06 12 20.20 13 20.26 6 11.80 4 5.95 11 19.74 9 17.71 10 18.91 7 14.14
[] y-hat = 3.20 + 1.4x [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. Create a scatterplot of the data. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] Identify a characteristic of the data that is ignored by the regression line. The data has a pattern that is not a straight line.
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
] Construct a scatterplot. Choose the correct graph below. [Copy Data to Statcrunch, Graph, Scatterplot, Chose proper X and Y columns, Compute, Compare]. [] The linear correlation coefficient is r = 0.937 [With the data in Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for "R (correlation coefficient) =" for the answer]. [] The critical values are r = -.811, .811. [] Because the absolute value of the linear correlation coefficient is _greater_ than the positive critical value, there _is_ sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of α = 0.05.
a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point with coordinates left parenthesis 1 comma 2 right parenthesis, use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b).
a. What is the equation of the regression line for all 10 points? y-hat = 2.766 + 0.766x [Manually insert the data points into Statcrunch, Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation and that is your answer]. [] b. What is the equation of the regression line for the set of 9 points? y-hat = 6 [In Statcrunch remove the outlier data set from the columns and continue with the same steps: Stat, Regression, Simple Linear, Chose proper X and Y columns, Compute, Under "Simple linear regression results" look for the only equation, then solve the equation: 6 + 0x, which would equal 6]. [] c. Choose the correct description of the results below. The removal of the point has a significant impact on the regression line.
Consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the accompanying technology output. Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not?
[] Choose the correct answer below. Yes, the multiple regression equation should be used for predicting the height of a son based on the height of his father and mother because the P-value in the ANOVA table is very low.
