Suppose a statistician built a multiple regression model for predicting the tota
ID: 3296855 • Letter: S
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
nequals=200200
samples, the results below were obtained. Complete parts a through
d.
Ind. Var.Ind. Var.
beta estimate nbsp estimate
Standard Error nbspStandard Error
Ind. Var.Ind. Var.
beta estimate nbsp estimate
Standard Error nbspStandard Error
InterceptIntercept
3.543.54
11.9611.96
Doubles left parenthesis x 3 right parenthesisDoubles x3
0.650.65
0.050.05
Walks left parenthesis x 1 right parenthesisWalks x1
0.290.29
0.060.06
Triples left parenthesis x 4 right parenthesisTriples x4
1.061.06
0.190.19
Singles left parenthesis x 2 right parenthesisSingles x2
0.490.49
0.050.05
Home Runs left parenthesis x 5 right parenthesisHome Runs x5
1.431.43
0.040.04
a. Write the least squares prediction equation for
yequals=total
number of runs scored by a team in a season.
ModifyingAbove y with caret equals nothing plus left parenthesis nothing right parenthesis x 1 plus left parenthesis nothing right parenthesis x 2 plus left parenthesis nothing right parenthesis x 3 plus left parenthesis nothing right parenthesis x 4 plus left parenthesis nothing right parenthesis x 5y=3.54+.29x1+.49x2+.65x3+1.06x4+1.43x5
(Type integers or decimals.)
b. Interpret, practically,
ModifyingAbove beta with caret 00
and
ModifyingAbove beta with caret 11
in the model. Which statement below best interprets
ModifyingAbove beta with caret 00?
A.
For a decrease of 1 in any variable, the runs scored changes by
ModifyingAbove beta with caret 00.
B.
For an increase of 1 in any variable, the runs scored changes by
ModifyingAbove beta with caret 00.
C.
For a change of
ModifyingAbove beta with caret 00
in any variable, the runs scored decreases by 1.
D.
For a change of
ModifyingAbove beta with caret 00
in any variable, the runs scored increases by 1.
E.
This parameter does not have a practical interpretation.
Which statement below best interprets
ModifyingAbove beta with caret 11?
A.
For a change of
ModifyingAbove beta with caret 11
in the number of walks, the runs scored decreases by 1.
B.
For a change of
ModifyingAbove beta with caret 11
in the number of walks, the runs scored increases by 1.
C.
For an increase of 1 in the number of walks, the runs scored changes by
ModifyingAbove beta with caret 11.
D.
For a decrease of 1 in the number of walks, the runs scored changes by
ModifyingAbove beta with caret 11.
E.
This parameter does not have a practical interpretation.
c. Conduct a test of
Upper H 0 : beta 5 equals 0H0: 5=0
against
Upper H Subscript a Baseline : beta 5 not equals 0Ha: 50
at
alphaequals=0.010.01.
The test statistic is
4.8334.833.
(Round to three decimal places as needed.)
The p-value is
nothing.
(Round to three decimal places as needed.)
Reject
Do not reject
the null hypothesis. There
is
is not
sufficient evidence to support the alternative hypothesis.d. Form a
9090%
confidence interval for
beta 22.
Interpret the results.
left parenthesis nothing comma nothing right parenthesis,
(Round to three decimal places as needed.)
Interpret this interval.
We are
nothing%
confident that the true value of
beta 22
lies in this interval.
(Type a whole number.)
Ind. Var.Ind. Var.
beta estimate nbsp estimate
Standard Error nbspStandard Error
Ind. Var.Ind. Var.
beta estimate nbsp estimate
Standard Error nbspStandard Error
InterceptIntercept
3.543.54
11.9611.96
Doubles left parenthesis x 3 right parenthesisDoubles x3
0.650.65
0.050.05
Walks left parenthesis x 1 right parenthesisWalks x1
0.290.29
0.060.06
Triples left parenthesis x 4 right parenthesisTriples x4
1.061.06
0.190.19
Singles left parenthesis x 2 right parenthesisSingles x2
0.490.49
0.050.05
Home Runs left parenthesis x 5 right parenthesisHome Runs x5
1.431.43
0.040.04
Explanation / Answer
a) y^ = 3.54 + 0.29 *x1 + 0.49 *x2 + 0.65*x3 + 1.06*x4 + 1.43*x5
b) b0 , when every independent variable is 0 . then y^ = b0
here option E) is correct
b1-
option C) is correct
For an increase of 1 in the number of walks, the runs scored changes by
ModifyingAbove beta with caret 11.
c)
TS = TS = b5^/(se(b5^) = 4.833
df = n-k-1 = 200-5-1 = 194
p-value = 2 P(t > 4.8333) = 0.0000
since p-value < 0.01
we reject the null hypothesis
there is sufficient evidence to support the alternative hypothesis
d)
90% confidence interval for b2
t* = 1.645
(0.49 - 1.645* 0.05), (0.49 + 1.645* 0.05)
=(0.40775, 0.57225 )
we are 90% confident confident that the true value of
2 lies in this interval.
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