SUMMARY OUTPUT

Regression Statistics

Multiple R0.420288912

R Square0.17664277

Adjusted R Square 0.174563585

Standard Error 2.505457775

Observations 398

ANOVA

dfSMSFSignificance F

Regression 1533.3065575533.306557584.957700251.82309E-18

Residual 3962485.8181916.277318665

Total 3973019.124749

CoefficientsStandard Errort Stat P-valueLower 95%

Intercept12.08113320.39860872930.308250473.1867E-10511.29747935

Upper 95%Lower 90.0% Upper 90.0%

12.8647870411.4239427612.73832363

X Variable 10.1482892020.0160882269.2172501461.82309E-180.116660191

Upper 95%Lower 90.0% Upper 90.0%

0.1799182140.1217643740.174814031

Among the many attributes of cars that impact fuel efficiency, the ability to accelerate from 0-to-60 MPH is rarely discussed. Download that data set that follows. Then run a regression analysis predicting fuel efficiency as measured by MPG based on Acceleration time as a predictor.Your results will be used in the next several problems.

1)How much correlation is there between the variables?

Round to three decimals and use leading zeros if necessary.

2)How much of the variability in MPG is explained by acceleration?

Round to three decimals and use leading zeros if necessary.

3) What is your decision regarding the null hypothesis of₁?

Reject the null becausep> 0.05.

Reject the null becausep< 0.05

Fail to reject the null becausep> 0.05

Fail to reject the null becausep< 0.05

4) What are the degrees of freedom for the t-test of 1?

5) Using only the confidence interval approach, at = 0.05, the conclusion about the₁hypothesis test is:

Reject the null hypothesis because the value of the null is outside the interval.

Reject the null hypothesis because the value of the null is inside the interval.

Fail to reject the null hypothesis because the value of the null is outside the interval.

Fail to reject the null hypothesis because the value of the null is inside the interval.

6) What is the 90% confidence interval around ₁?

0952902 - 8.986684

0937129 - 1.44528

1.601134 - 8.338452

0.978131 - 1.404278

7) How are the degrees of freedom error computed?

n

n-1

k

k-1

n-k

n-k-1

8) At = 0.05, is the overall model significant?

No, F* < F_c

The test is inconclusive because 0.05 <p< 0.10

Yes, F* < F_c, andp< 0.05.

Yes, F* > F_c, andp< 0.05.

Yes, F* > F_c, andp> 0.05.

9) What is your decision about the null hypothesis for the overall model?

Reject the null

The test is inconclusive

Fail to reject

10) The model of the data is described by=+*x

Round each entry to three decimals.

11) Ifxis increased by one unit, how much doesy-hat increase?

Round to three decimals.

12) Predict the value of y given acceleration is 10.75.

Round to three decimals.