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.
