Chapter 10-2

Listed below are systolic blood pressure measurements​ (in mm​ Hg) obtained from the same woman. Find the regression​ equation, letting the right arm blood pressure be the predictor​ (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05. Right Arm Left Arm 103 177 102 171 94 148 76 147 76 145 The regression equation is y= _____ + ______x Given that the systolic blood pressure in the right arm is 85 mm Hg, the best predicted systolic blood pressure in the left arm is _____ mm Hg.

The regression equation is y= _70.1_ + _1.0_x StatCrunch, Stat, Regression, Simple Linear, Enter x and y, Compute. Given that the systolic blood pressure in the right arm is 85 mm Hg, the best predicted systolic blood pressure in the left arm is _____ mm Hg.

What is the difference between the following two regression​ equations? y=b0+b1x y=β0+β1x a) The first equation is for sample data; the second equation is for a population. b) The first equation is for a population; the second equation is for sample data.

a) The first equation is for sample data; the second equation is for a population.

What is the relationship between the linear correlation coefficient r and the slope b1 of a regression​ line? a) The value of r will always be larger than the value of b1. b) The value of r will always have the same sign as the value of b1. c) The value of r will always have the opposite sign of the value of b1. d) The value of r will always be smaller than the value of b1.

b) The value of r will always have the same sign as the value of b1.

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 7 13.61 13 16.25 10 16.64 3 4.25 9 16.01 6 11.84 11 16.90 4 7.16 5 9.70 8 15.01 12 16.76 y= ______ + _____x Identify a characteristic of the data that is ignored by the regression line. a) There is an influential point that strongly affects the graph of the regression line. b) The data has a pattern that is not a staight line. c) There is no trend in the data. d) There is no characteristic of the data that is ignored by the regression line.

y= _3.50_ + _1.2_x StatCrunch, Stat, Regression, Simple Linear, Enter x and y, then compute. Intercept and Slope Estimate is answer. Identify a characteristic of the data that is ignored by the regression line. b) The data has a pattern that is not a staight line.

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ lemon/crash data, where lemon imports are in metric tons and the fatality rates are per​ 100,000 people, find the best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports. Is the prediction​ worthwhile? Find the equation of the regression line. y= _____ + (_____)x The best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports is _____ fatalities per 100,000 population. Is the prediction worthwhile? a) Since all of the requirements for finding the equation of the regression line are​ met, the prediction is worthwhile. b) Since the sample size is​ small, the prediction is not appropriate. c) Since there appears to be an​ outlier, the prediction is not appropriate. d) Since common sense suggests there should not be much of a relationship between the two​ variables, the prediction does not make much sense.

Find the equation of the regression line. y= _16.563_ + (_-0.002724_)x StatCrunch, Stat, Regression, Simple Linear, Enter Lemon Imports for x, Enter Crash Fatality Rate for y. Estimates for slope and intercept. The best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports is _15.2_ fatalities per 100,000 population. Is the prediction worthwhile? d) Since common sense suggests there should not be much of a relationship between the two​ variables, the prediction does not make much sense.

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ actress/actor ages in various​ years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 27 years. Is the result within 5 years of the actual Best Actor​ winner, whose age was 45 years? Best Actress Best Actor 27 45 29 38 29 38 64 46 33 53 33 48 44 62 29 48 61 37 21 57 43 45 56 33 Find the equation of the regression line. y= _____ + (_____)x The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 27 year is _____ years old. Is the result within 5 years of the actual Best Actor winner, whose age was 45 years? _____ the predicted age is __________ the actual winner's age.

Find the equation of the regression line. y= _53.4_ + (_-0.194_)x StatCrunch, Stat, Regression, Simple Linear, Enter x and y, Compute. Estimates for slope and intercept answer. The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 27 year is _45_ years old. Is the result within 5 years of the actual Best Actor winner, whose age was 45 years? _Yes,_ the predicted age is _5 years or less from_ the actual winner's age.

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 10 7.28 8 6.45 13 13.23 9 6.76 10 8.17 14 9.18 5 5.89 4 5.14 11 8.47 6 6.54 6 5.81 Find the equation of the regression line. y= _____ + ______x Identify a characteristic of the data that is ignored by the regression line. a) The data has a pattern that is not a straight line. b) There is no trend in the data. c) There is no characteristic of the data that is ignored by the regression line. d) There is an influential point that strongly affects the graph of the regression line.

Find the equation of the regression line. y= _2.51_ + _0.575_x StatCruch, Stat, Regression, Simple Linear, Enter x and y, Compute. Intercept and Slope Estimate is answer. Identify a characteristic of the data that is ignored by the regression line. d) There is an influential point that strongly affects the graph of the regression line.

For a pair of sample​ x- and​ y-values, the __________ is the difference between the observed sample value of y and the​ y-value that is predicted by using the regression equation.

For a pair of sample​ x- and​ y-values, the _residual_ is the difference between the observed sample value of y and the​ y-value that is predicted by using the regression equation.

Given a collection of paired sample​ data, the ___________ y with carety=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

Given a collection of paired sample​ data, the _regression equation_ y with carety=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

Find the regression​ equation, letting the diameter be the predictor​ (x) variable. Find the best predicted circumference of a beachballbeachball with a diameter of 42.5 cm. How does the result compare to the actual circumference of 133.5 ​cm? Use a significance level of 0.05. Baseball D: 7.3 C: 22.9 Basketball D: 23.6 C: 74.1 Golf D: 4.3 C: 13.5 Soccer D: 22.1 C: 69.4 Tennis D: 7.1 C: 22.3 Ping-Pong D: 3.9 C: 12.3 Volleyball D: 21.2 C: 66.6 The regression equation is y= _____ + _____x The best predicted circumference for a diameter of 42.5 cm is _____ cm. How does the result compare to the actual circumference of 133.5 cm? a) Since 42.5 cm is within the scope of the sample​ diameters, the predicted value yields the actual circumference. b) Even though 42.5 cm is beyond the scope of the sample​ diameters, the predicted value yields the actual circumference. c) Since 42.5 cm is beyond the scope of the sample​ diameters, the predicted value yields a very different circumference. d) Even though 42.5 cm is within the scope of the sample​ diameters, the predicted value yields a very different circumference.

The regression equation is y= _0.01247_ + _3.13981_x StatCrunch, Stat, Regression, Simple Linear, Enter x and y, Enter predicted cir. The best predicted circumference for a diameter of 42.5 cm is _133.5_ cm. How does the result compare to the actual circumference of 133.5 cm? b) Even though 42.5 cm is beyond the scope of the sample​ diameters, the predicted value yields the actual circumference.

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 $100million. Use a significance level of α=0.05. Budget Gross 44 115 22 7 116 93 68 68 77 112 49 107 118 103 65 90 6 49 56 112 127 219 23 34 5 11 153 292 5 48 The regression equation is y= _____ + _____x. The best predicted gross for a movie with a $100 million budget is $_____ million.

The regression equation is y= _16.3_ + _1.3_x. The best predicted gross for a movie with a $100 million budget is $_146.1_ million.

What is a residual? a) A residual is a point that has a strong effect on the regression equation. b) A residual is a value of y − y with carety​, which is the difference between an observed value of y and a predicted value of y. c) A residual is a value that is determined​ exactly, without any error. d) A residual is the amount that one variable changes when the other variable changes by exactly one unit. 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 __________ of the residuals is the __________ possible sum.

What is a residual? b) A residual is a value of y − y with carety​, which is the difference between an observed value of y and a predicted value of y. 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.

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 44 inches. Is the result close to the actual weight of 233 pounds? Use a significance level of 0.05. Chest Size Weight 50 321 41 221 45 265 52 335 45 307 45 265 What is the regression equation? y= _____ + _____x The best predicted weight for a bear with a chest size of 44 inches is ______ pounds. Is the result close to the actual weight of 233 pounds? a) This result is very close to the actual weight of the bear. b) This result is close to the actual weight of the bear. c) This result is exactly the same as the actual weight of the bear. d) This result is not very close to the actual weight of the bear.

What is the regression equation? y= _-170.3_ + _9.8_x StatCrunch, Stat, Regression, Simple Linear, Enter x and y, Compute. Intercept and Slope Estimate is the answer. The best predicted weight for a bear with a chest size of 44 inches is _262.7_ pounds. Is the result close to the actual weight of 233 pounds? d) 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? What is the regression equation? y= _____ + _____x The best predicted temperature when a bug is chirping at 3000 chirps per minute is _____ °F. What is wrong with this predicted​ value? Choose the correct answer below. a) It is only an approximation. An unrounded value would be considered accurate. b) It is unrealistically high. The value 3000 is far outside of the range of observed values. c) The first variable should have been the dependent variable. d) Nothing is wrong with this value. It can be treated as an accurate prediction.

What is the regression equation? y= _33.03_ + _0.0456_x StatCrunch, Stat, Regression, Simple Linear, Enter x and y, Enter y prediction. The best predicted temperature when a bug is chirping at 3000 chirps per minute is _169.9_ °F. What is wrong with this predicted​ value? Choose the correct answer below. b) It is unrealistically high. The value 3000 is far outside of the range of observed values.