Question

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   Miles per Gallon, y
3736 17
3938 17
2746 24
3485 19
3250 22
3035 24
3826 16
2506 23
3387 18
3847 18
3251 17

​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

y^= (BLANK, round to 5 decimal places as needed)x + (BLANK, round 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 answer from part A to find this answer)

A. A weightless car will get (BLANK) 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 (BLANK) ​mile(s) per​ gallon, on average. A weightless car will get (BLANK)

miles per​ gallon, on average.

C. For every pound added to the weight of the​ car, gas mileage in the city will decrease by (BLANK) ​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.

​(c) A certain​ gas-powered car weighs 3700 pounds and gets 20 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight?

A. Above

B. Below

​(d) Would it be reasonable to use the​ least-squares regression line to predict the miles per gallon of a hybrid gas and electric​ car? Why or why​ not?

A.​ No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of n =11.

B.​Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n =11.

C. ​No, because the hybrid is a different type of car.

D. ​Yes, because the hybrid is partially powered by gas.

Answer 1

a)

y^ =-0.00553x+38.15

b)

C. For every pound added to the weight of the​ car, gas mileage in the city will decrease by 0.00553 mile(s) per​ gallon, on average. It is not appropriate to interpret the​ y-intercept.

c)

predicted val=38.15+3700*-0.00553=

17.6890

since 20 is above the predicted value

A. Above

d)

C. ​No, because the hybrid is a different type of car.