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A consumer organization wants to develop a regression model to predict gasoline​mileage​ (as measured by miles​ per​ gallon) based on the horsepower of​ the​ car’s engine and the weight of the​ car​ (in​pounds).

/in /by

A consumer organization wants to develop a regression model to predict gasoline​mileage​ (as measured by miles​ per​ gallon) based on the horsepower of​ the​ car’s engine and the weight of the​ car​ (in​pounds). A sample of 20 recent car models​was​ selected, with the results recorded in the accompanying table.
The resulting ANOVA table is below. Complete parts​ (a) through​ (c).
Regression
Statistics
Multiple R
0.9770

R Square
0.9546

n
8

Source

Regression

Degrees of
Freedom
2

Sum of
Squares
16.94097

Mean Square
8.47049
F
52.56
p-value
0.0004
Error

Degrees of
Freedom
5

Sum of
Squares
0.80575

Mean Square
0.16115

total
Degrees of
Freedom

7

Sum of
Squares
17.74672

a. Determine whether the model is significant​ (overall) at the
0.05 level of significance. Choose the correct answer below.
A.
Do not reject H0. There is insufficient evidence to prove that at least one slope is not zero. We cannot prove that there is a linear relationship between mileage and at least one of the horsepower and weight.
B. Reject H0. There is insufficient evidence to prove that at least one slope is not zero. We cannot prove that there is a linear relationship between mileage and at least one of horsepower and weight.
C. Reject H0. There is sufficient evidence to prove that at least one slope is not zero.  There is a linear relationship between mileage and at least one of horsepower and weight.
D. Do not reject H0. There is sufficient evidence to prove that at least one slope is not zero.  There is a linear relationship between mileage and at least one of horsepower and weight.

b. What is the value coefficient of multiple​determination, R2, and interpret its meaning.

R2=

(Round to four decimal places as​needed.)
c. Interpret the meaning of R2.
It indicates that ___% of the variation in mileage in the sample can be explained by its linear relationship with horsepower and weight.
​(Round to two decimal places as​ needed.)

 
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