Question

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.	β estimate	Standard Error	Ind. Var..	β estimate	Standard Error
Intercept	3.92	13.05	Doubles x3	0.63	0.02
Walks x1	0.22	0.05	Triples x4	1.15	0.17
Singles x2	0.43	0.05	Home runs (x5)	1.54	0.02

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 ofModifyingAbove beta with caret β0 in any​ variable, the runs scored decreases by 1.

B.For a change of β0 0in any​ variable, the runs scored increases by 1.

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

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

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 decreases by 1.

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

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

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

E.This parameter does not have a practical interpretation.

c. Conduct a test of H0: β4=0 against Ha: β4>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.)

▼

(Do not reject,Reject) the null hypothesis. There (is is not) sufficient evidence to support the alternative hypothesis.d. Form a 95​% confidence interval for β1.

Interpret the results.

(___________,,___________) ​(Round to three decimal places as​ needed.

Interpret this interval.

We are________​% confident that the true value of β1 lies in this interval. ​(Type a whole​ number.)

Answer 1

a) y=3.92+0.22x1+0.43x2+0.63x3+1.15x4+1.54x5

b) Which statement below best interprets β0​?

E.This parameter does not have a practical interpretation.

Which statement below best interprets β1​?

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

c)

The test statistic is 1.15/0.17=6.765

The​ p-value is =0.0000

Reject) the null hypothesis. There is sufficient evidence to support the alternative hypothesis.

95​% confidence interval for β1. =-21.815 ; 29.655

We are_95__​% confident that the true value of β1 lies in this interval.