9. An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weight of various cars and their gas mileage. Miles per Car Weight (pounds) Gallon A 3590 18 B 2690 26 C 3180 23 D 3565 20 E 3680 19 a. Determine which variable is the likely explanatory variable and which is the likely response variable. Circle one! i. The explanatory variable is the miles per gallon and the response variable is the weight. ii. The explanatory variable is the weight and the response variable is the miles per gallon. b. Find the equation of the least-squares regression line. You can use calculator. Round to three decimal places! c. Interpret the slope. d. Interpret the y-intercept. e. Use the regression equation to predict the MPG of a car that is 3180 lbs.
Added by Michelle P.
Close
Step 1
Step 1: The explanatory variable is the weight of the car, and the response variable is the miles per gallon. Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 66 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying data represent the weights of various domestic cars and their gas mileages in the city for a certain model year. Complete parts (a) through (d) below. Click here to view the car data. Click here to view the table of critical values of the correlation coefficient. (a) Determine which variable is the likely explanatory variable and which is the likely response variable. Choose the correct answer below. The explanatory variable is the weight and the response variable is the miles per gallon. The explanatory variable is the miles per gallon and the response variable is the weight. (b) Draw a scatter diagram of the data. Choose the correct graph below. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. r = (Round to three decimal places as needed.) (d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon based on the scatter diagram and the linear correlation coefficient. The variables weight of a car and its miles per gallon are associated because r is and the absolute value of the correlation coefficient is than the critical value. (Round to three decimal places as needed.)
Supreeta N.
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Weight (pounds), x Miles per Gallon, y 3787 18 3798 17 2725 24 3460 19 3334 20 3028 24 3808 18 2703 25 3570 19 3836 17 3370 18 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Å· = -0.00669x + 42.68 (Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. For every pound added to the weight of the car, gas mileage in the city will decrease by __?__ mile(s) per gallon, on average. A weightless car will get __?__ miles per gallon, on average. B. A weightless car will get __?__ miles per gallon, on average. It is not appropriate to interpret the slope. C. For every pound added to the weight of the car, gas mileage in the city will decrease by __?__ mile(s) per gallon, on average. It is not appropriate to interpret the y-intercept. D. It is not appropriate to interpret the slope or the y-intercept.
Sheryl E.
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. Weight (pounds), x 3832 17 3911 17 2757 24 3637 18 3402 22 2941 22 3796 18 2701 24 3403 19 3879 16 3274 17 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=_____x+ (Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. A weightless car will get nothing miles per gallon, on average. It is not appropriate to interpret the slope. B. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on average. A weightless car will get nothing miles per gallon, on average. C. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on average. It is not appropriate to interpret the y-intercept. D. It is not appropriate to interpret the slope or the y-intercept.
Ariana N.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD