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	3.88	17.03	Doubles (X3)	0.74	0.04
Walks (X1)	0.37	0.05	Triples (X4)	1.17	0.23
Singles (X2)	0.51	0.05	Home Runs (X5)	1.44	0.04

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

y=(3.88)+(0.37)X1+(0.51)X2+(0.74) X3+(1.17).X4+(1.44) X5. CORRECT ANSWERS (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 increases 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 decreases by 1.

E. This parameter does not have a practical interpretation. Your answer is correct.

Which statement below best interprets β1?

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

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

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

D. For a change of β1in the number of walks, the runs scored decreases by 1.

E. This parameter does not have a practical interpretation.

Answer 1

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

this is correct: y=(3.88)+(0.37)X1+(0.51)X2+(0.74) X3+(1.17).X4+(1.44) X5.

Each variable is multiplied my its respective coefficient and added to the interscept to give the predicted runs scored

CORRECT ANSWERS (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 increases 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 decreases by 1.

E. This parameter does not have a practical interpretation. Your answer is correct.

Reason:

Bo is the intersect' coefficient and basically doesn't have any impact on dependent variable from changes in value of any variables.

Which statement below best interprets β1?

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

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

C. For a decrease 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 decreases by 1.

E. This parameter does not have a practical interpretation.

In particular the 1 unit increase in variable X1 will increase the runs scored by β1 units