A multiple linear regression model was developed between response variable Y and
ID: 2907290 • Letter: A
Question
A multiple linear regression model was developed between response variable Y and independent variables X1, and X2. The regression analysis results are summarized in the following table.
There are some missing values in the table. The following question asked you to fill out some of the missing values.
Regression Statistics
Multiple R
0.9905
R Square
0.9811
Adjusted R Square
0.9794
Standard Error
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
Residual
115.173
Total
6105.945
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
2.2638
1.0601
2.136
0.0441
0.06535
4.46223
X1
2.55031
2.93823
X2
0.0125
0.0028
The t- statistic of the coefficient for X1 (B1 ) is equal to
A. 29.343
B. 3.753
C. 29.836
D. 5.324
Regression Statistics
Multiple R
0.9905
R Square
0.9811
Adjusted R Square
0.9794
Standard Error
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
Residual
115.173
Total
6105.945
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
2.2638
1.0601
2.136
0.0441
0.06535
4.46223
X1
2.55031
2.93823
X2
0.0125
0.0028
Explanation / Answer
here coefficient for X1 =(LCL+UCL)/2 =(2.55031+2.93823)/2=2.74427
also margin of error =(UCL-LCL)/2 =(2.93823-2.55031)/2=0.19396
for 95% CI and (n-p-1=22) degree of freedom crtiical t =2.074
hence std error =margin of error/crtiical t =0.19396/2.074=0.09352
therefore t- statistic of the coefficient for X1 =coefficient/std error =2.74427/0.09352=29.343
option A is correct
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