Based on a series of repeated test drives of a new Equus at constant speeds betw

Question

Based on a series of repeated test drives of a new Equus at constant speeds between 30 and 80 miles per hour, the equation of a simple linear regression line modeling miles per gallon (mpg) vs. speed driven (mph) is given by: mpg-32 - (0.12 x mph). Use this information to answer questions 17-20. 17. An Equus driven at a constant speed of 70 mph will: A. get 1.2 mpg more than one driven at a constant speed of 80 mph B. get 1.2 mpg less than one driven at a constant speed of 80 mph C. be expected to get 1.2 mpg more than one driven at a constant speed of 80 mph. D. be expected to get 1.2 mpg less than one driven at a constant speed of 80 mph. E. be expected to get 8.4 mpg more than one driven at a constant speed of 80 mph

Explanation / Answer

(17) right choice is C. expected to get 1.2 mpg more .........of 80 mph

here mpg=30=0.12*mph

for mph=70, mpg=30-0.12*70=21.6

for mph=80, mpg=30-0.12*7=20.4

(18) B.negative

the regression coefficient =r*sd(mph)/sd(mpg)=-0.12 is negative and function of correlation coefficeint, here regression coefficeint is negative so corrleation coefficient will be negative

(19) right choice is B. the car was never driven at 120 mph during the test

(20) In all linear regression models, the intercept has the same definition: the mean of the response, Y, when all predictors, all X = 0.

here if mph=0 the mpg=32, so when speed is zero the mile per gallon =32 has no practical meaning in predication.

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