hw 9.2

Using the scatter plot of the registered nurse salary data​ shown, what type of​ correlation, if any do you think the data​ have? Explain. A. There appears to be a strong positive linear correlation. As the years of experience of the registered nurses​ increase, salaries tend to increase. B. There appears to be a strong positive linear correlation. As the years of experience of the registered nurses​ increase, salaries tend to decrease. C. There appears to be a strong negative linear correlation. As the years of experience of the registered nurses​ increase, salaries tend to decrease. D. There does not appear to be any linear correlation.

A. There appears to be a strong positive linear correlation. As the years of experience of the registered nurses​ increase, salaries tend to increase.

Is it appropriate to use a regression line to predict​ y-values for​ x-values that are not in​ (or close​ to) the range of​ x-values found in the​ data? Choose the correct answer below. A. It is appropriate because the regression line models a​ trend, not the actual​ points, so although the prediction of the​ y-value may not be exact it will be precise. B. It is not appropriate because the regression line models the trend of the given​ data, and it is not known if the trend continues beyond the range of those data. C. It is not appropriate because the correlation coefficient of the regression line may not be significant. D. It is appropriate because the regression line will always be​ continuous, so a​ y-value exists for every​ x-value on the axis.

B. It is not appropriate because the regression line models the trend of the given​ data, and it is not known if the trend continues beyond the range of those data.

Given a set of data and a corresponding regression​ line, describe all values of x that provide meaningful predictions for y. A. Prediction values are meaningful for all​ x-values that are realistic in the context of the original data set. B. Prediction values are meaningful only for​ x-values in​ (or close​ to) the range of the original data. Your answer is correct. C. Prediction values are meaningful only for​ x-values that are not included in the original data set.

B. Prediction values are meaningful only for​ x-values in​ (or close​ to) the range of the original data. Your answer is correct.

18 A linear equation is an equation of the form y=ax+b​, and a power equation is an equation of the form y=axb. The linear equation and power equation for the accompanying data are provided below. Determine which equation is a better model for the data. Explain your reasoning. x 1 2 3 4 5 6 7 8 y 695 407 239 108 81 77 69 75 Choose the correct answer below. A. The linear equation is a better model for the data because the graph of the linear equation fits the data better than the graph of power equation. B. The power equation is a better model for the data because the graph of the power equation fits the data better than the graph of linear equation. Your answer is correct. C. The linear equation is a better model for the data because the graph of the linear equation passes through more data points than the graph of power equation. D. The power equation is a better model for the data because the graph of the power equation has more data points above the line than the graph of linear equation.

B. The power equation is a better model for the data because the graph of the power equation fits the data better than the graph of linear equation.

Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or​ negative? A. The slope is negative. As the independent variable increases the dependent variable also tends to increase. B. The slope is positive. As the independent variable increases the dependent variable tends to decrease. C. The slope is positive. As the independent variable increases the dependent variable also tends to increase. Your answer is correct. D. The slope is negative. As the independent variable increases the dependent variable tends to decrease.

C. The slope is positive. As the independent variable increases the dependent variable also tends to increase.

Explain how to predict​ y-values using the equation of a regression line. Choose the correct answer below. A. Use the graph of the regression line to determine the​ x-value that corresponds to the​ y-value for which you are solving. B. Substitute the correlation coefficient into the equation and solve for y. C. Substitute a value of y into the equation of a regression line and solve for x. D. Substitute a value of x into the equation of a regression line and solve for y.

D. Substitute a value of x into the equation of a regression line and solve for y.

In order to predict​ y-values using the equation of a regression​ line, what must be true about the correlation coefficient of the​ variables? Choose the correct answer below. A. The correlation between variables must be an​ x-value of a point on the graph. B. The correlation between variables must be greater than zero. C. The correlation between variables must be a​ y-value of a point on the graph. D. The correlation between variables must be significant.

D. The correlation between variables must be significant.

An analyst used the regression line for the data to the right to predict the annual salary for a registered nurse with 28 years of experience. Is this a valid​ prediction? Explain your reasoning. A. ​Yes, the prediction is meaningful because x=28 is not part of the original data set. B. ​Yes, the prediction is meaningful because x=28 makes sense in the context of the original data set. C. ​No, the prediction is not meaningful because the regression line may not be used to generate meaningful predictions. D. ​No, the prediction is not meaningful because x=28 is outside the range of the original data set.

D. ​No, the prediction is not meaningful because x=28 is outside the range of the original data set.

Use the data in the table below to complete parts​ (a) through​ (d). x 37 34 41 45 42 50 60 56 52 y 25 23 27 32 30 30 28 24 27

STAT EDIT STAT CALC (a) Find the equation of the regression line. STAT EDIT enter data into L1 & L2 STAT CALC 4: LinReg (ax+b) ENTER ŷ = .072x + (24.013) (b) Construct a scatter plot of the data and draw the regression line. Plot the​ x-values on the horizontal axis and the​ y-values on the vertical axis. ZOOM 9 A. (see image) (c) Construct a residual plot. Plot the​ x-values on the horizontal axis and the residuals on the vertical axis. Choose the correct graph below. STAT CALC 8: LinReg (a+bx) ENTER ZOOM 9 B. (see image) ​(d) Determine if there are any patterns in the residual plot and explain what they suggest about the relationship between the variables. The residual plot shows a pattern because the residuals do not fluctuate about 0. This implies the regression line is not a good representation of the relationship between the variables.

Use the data shown in the table. Replace each​ x-value and​ y-value in the table with its logarithm. Find the equation of the regression line for the transformed data. Then construct a scatter plot of (log x,logy) and sketch the regression line with it. What do you​ notice? x 1 2 3 4 5 6 7 8 y 1064 462 305 209 146 103 94 66

STAT EDIT STAT CALC (a) find the equation of the regression line of the transformed data STAT EDIT Input info into L1 & L2 at the top of L3 lOG L1 ENTER at the top of L4 LOG L2 ENTER STAT CALC 4: LinReg (ax+b) L3, L4 ENTER log y=−1.311 logx+3.063 (b) construct a scatterplot of (log x,logy) with the values of logx on the horizontal axis and the values of logy on the vertical axis and sketch the regression line with it. D (see image) (c) What do you​ notice? The graph to the right is a scatterplot of the untransformed data with the​ x-values on the horizontal axis and the​ y-values on the vertical axis along with the resulting regression line A linear model is more appropriate for the transformed data than for the untransformed data.

17 A power equation is a nonlinear regression equation of the form y=ax^b. Use a technology tool to find and graph the power equation for the data below. Include a scatter plot in your graph. Note that you can also find this model by solving the equation logy = m(log x)+b. x 1 2 3 4 5 6 7 8 y 681 415 255 120 92 72 61 77

STAT EDIT STAT CALC (a) find the graph Input data into L1 & L2 STAT EDIT ZOOM 9 D (see image) (b) Find the power equation STAT CALC A: PwrReg y=a*x^b ENTER y = (789.99)_x^-1.25

Complete parts​ (a) through​ (c) using the following data. Row 1 2 3 3 3 3 5 5 6 7 7 Row 2 90 84 77 72 90 75 79 80 63 62

STAT EDIT STAT CALC LineRegR (a) Find the equation of the regression line for the given​ data, letting Row 1 represent the​ x-values and Row 2 the​ y-values. Sketch a scatter plot of the data and draw the regression line. STAT EDIT input data into L1 & L2 STAT CALC 4: LinReg (ax+b) ENTER ŷ = -4.039x + (94.974) (b) choose the correct graph (see image) ​(c) Find the equation of the regression line for the given​ data, letting Row 2 represent the​ x-values and Row 1 the​ y-values. Sketch a scatter plot of the data and draw the regression line. STAT CALC 8: LinReg (a+bx) ENTER ŷ = -.145x + (15.558) (d)​choose the correct graph (see image) (e) ​What effect does switching the explanatory and response variables have on the regression​ line? The sign of m is​ unchanged, but the values of m and b change.

The accompanying data are the number of wins and the earned run averages​ (mean number of earned runs allowed per nine innings​ pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not. ​(a) x=5 wins ​(b) x=10 wins ​(c) x=19 wins ​(d) x=15 wins ​Wins, x 20 18 17 16 14 12 11 9 Earned run​ average, y 2.79 3.27 2.66 3.82 3.86 4.26 3.72 5.11

STAT EDIT STAT CALC LineRegR (a) find the regression equation STAT EDIT input data into L1 & L2 STAT CALC 4: LinReg (ax+b) ENTER ŷ = -.18x + (6.35) (b) choose the correct graph C (see image) (c)​Predict value of y for x=5. PRGM LineRegR A=-.18 B=6.35 X=5 It is not meaningful to predict this value of y because x=5 is well outside the range of the original data. (d) Predict value of y for x=10 PRGM LineRegR A=-.18 B=6.35 X=10 ŷ = 4.55 (e) Predict value of y for x=19 PRGM LineRegR A=-.18 B=6.35 X=19 ŷ = 2.93 (f) Predict value of y for x=15 PRGM LineRegR A=-.18 B=6.35 X=15 ŷ = 3.65

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (The pair of variables have a significant​ correlation.) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The table below shows the heights​ (in feet) and the number of stories of six notable buildings in a city. Height, x 758 621 518 510 492 483 ​Stories, y 51 47 46 43 37 36 ​(a) x=503 feet ​(b) x=650 feet​ (c) x=315 feet ​(d) x=735 feet

STAT EDIT STAT CALC LineRegR (a) find the regression equation STAT EDIT input data into L1 & L2 STAT CALC 4: LinReg (ax+b) ENTER ŷ = .046x + (17.51) (b) choose the correct graph C (see image) (c)​Predict value of y for x=503. PRGM LineRegR A=.046 B=17.51 X=503 y = 41 (d) Predict value of y for x=650 PRGM LineRegR A=.046 B=17.51 X=650 y = 47 (e) Predict value of y for x=315 PRGM LineRegR A=.046 B=17.51 X=315 y = not meaningful (f) Predict value of y for x=735 PRGM LineRegR A=.046 B=17.51 X=735 y = 51

14 Use the data in the table below to complete parts​ (a) through​ (c). x 4 6 9 11 13 16 20 46 y 26 31 27 31 21 22 22 7

STAT EDIT STAT CALC (a) construct a scatterplot STAT EDIT enter data into L1 & L2 STAT CALC 4: LinReg (ax+b) ENTER ŷ = -.532x + (31.69) ZOOM 9 D. (see image) (b) identify any possible outliers A. The point (46,7) may be an outlier. (c) Determine if the point is influential. The change in slope or intercept is significant if it is larger than 10%. STAT EDIT modify L1 & L2 by deleting the outlier then, STAT CALC 4: LinReg (ax+b) ENTER ŷ = -.493x + (31.28) equation with outlier is ŷ = -.532x + (31.69) (from above) equation w/out outlier is ŷ = -.493x + (31.28) The point is not an influential point because the slopes with the point included and without the point included are not significantly​ different, and the intercepts are not significantly different.

An exponential equation is a nonlinear regression equation of the form y=abx. Use technology to find and graph the exponential equation for the accompanying​ data, which shows the number of bacteria present after a certain number of hours. Include the original data in the graph. Note that this model can also be found by solving the equation log y=mx + b for y. Number of​ hours, x 1 2 3 4 5 6 7 Number of​ bacteria, y 167 279 469 781 1313 1923

STAT EDIT STAT CALC ExpReg Input data into L1 & L2 STAT CALC 0: ExpReg (a*b^x) ŷ = 93.65x + (1.71) ZOOM 9 Choose the correct graph (see image)

Match the description with its symbol.

see image

Match the regression equation with the appropriate graph.

see image