Question

# Suppose a statistician built a multiple regression model for predicting the total number of runs scored...

Suppose a statistician built a multiple regression model for predicting the total number of runs scored by a baseball team during a season. Using data for n=200 ​samples, the results below were obtained. Complete parts a through d.

 Ind. Var.I β estimate Standard Error Ind. Var.. β estimate Standard Error Intercept 3.75 13.19 Doubles (x3) 0.63 0.03 Walks (x1) 0.23 0.04 Triples (x4) 1.02 0.21 Singles x2 0.42 0.05 Home Runs (x 5) 1.59 0.05

a. Write the least squares prediction equation for y = total number of runs scored by a team in a season.

y=+x1+x2+x3+x4+x5 (Type integers or​ decimals.)

b.​ Interpret, practically, β0 and β1 in the model. Which statement below best interprets β0​?

A.For a change of β0 in any​ variable, the runs scored decreases by 1.

B.For a decrease of 1 in any​ variable, the runs scored changes by β0.

C.For an increase of 1 in any​ variable, the runs scored changes by β0.

D.For a change of β0 in any​ variable, the runs scored increases by 1.

E.This parameter does not have a practical interpretation.

Which statement below best interprets β1​?

A.For a change of β1 in the number of​ walks, the runs scored increases by 1.

B.For an increase of 1 in the number of​ walks, the runs scored changes by β1.

C.For a change of β1 in the number of​ walks, the runs scored decreases by 1.

D.For a decrease of 1 in the number of​ walks, the runs scored changes by β1.

E. This parameter does not have a practical interpretation.

c. Conduct a test of H0: β3=0 against Ha: β3>0 at α=0.01 The test statistic is (_______).​(Round to three decimal places as​ needed.)

The​ p-value is (________)​(Round to three decimal places as​ needed.)

(Reject Do not reject) the null hypothesis. There

(is not, is) sufficient evidence to support the alternative hypothesis.d. Form a 90​% confidence interval for β5.

Interpret the results.  (______, __________),Round to three decimal places as​ needed.)

Interpret this interval.

We are(________)​% confident that the true value of β5 lies in this interval. ​(Type a whole​ number.)

b.

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