Stats Quiz 4: Correlation & Regression (Ch 4)

The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=−0.981. The​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=−0.0069x+44.6554. Complete parts ​(a) and ​(b) below. ​(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per​ gallon? ​(b) Interpret the coefficient of determination.

a. The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is 96.2 % (r=-0.981, r^2=0.962) b. 96.2% of the variance in gas mileage is explained by the linear model.

An engineer wants to determine how the weight of a​ car, x, affects gas​ mileage, y. The following data represent the weights of various cars and their miles per gallon. Car A B C D E Weight​ (lbs), x 2635 3045 3375 3770 4135 Miles p Gallon, y 27.1 26.7 25 24.7 19.5 ​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ​(b) Interpret the slope and​ intercept, if appropriate. Choose the best interpretation for the slope. Choose the best interpretation for the​ y-intercept. ​(c) Predict the miles per gallon of car D and compute the residual. Is the miles per gallon of this car above average or below average for cars of this​ weight? Is the value above or below​ average? ​(d) Draw the​ least-squares regression line on the scatter diagram of the data and label the residual. Which of the following represents the data with the residual shown in​ red?

a. Write the equation for the​ least-squares regression line. y=-0.00459x + 40.2 b.The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. It is not appropriate to interpret the​ y-intercept because it does not make sense to talk about a car that weighs 0 pounds. c. The predicted value is 22.86 miles per gallon. The residual is 1.84 miles per gallon. It is above average. d. b

Match the linear correlation coefficient to the scatter diagram. The scales on the​ x- and​ y-axis are the same for each scatter diagram. (a) r=−0.810​, (b) r=−1​, (c) r=−0.049

​(a) Scatter diagram II. ​(b) Scatter diagram I. ​(c) Scatter diagram III.