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From the data below;2Х13454уг861215a) Compute the mean square errorb) Compute the standard error of the estimatec) Compute the estimated standard deviation of bld) Use the t-test to test the following hypothesis (a .05)Ho B1 0Ha: Bl 0e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present inthe analysis of variance format

Question
From the data below;
2
Х1
3
4
5
4
уг
8
6
12
15
a) Compute the mean square error
b) Compute the standard error of the estimate
c) Compute the estimated standard deviation of bl
d) Use the t-test to test the following hypothesis (a .05)
Ho B1 0
Ha: Bl 0
e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present in
the analysis of variance format
help_outline

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From the data below; 2 Х1 3 4 5 4 уг 8 6 12 15 a) Compute the mean square error b) Compute the standard error of the estimate c) Compute the estimated standard deviation of bl d) Use the t-test to test the following hypothesis (a .05) Ho B1 0 Ha: Bl 0 e) Use the F-test to test the hypotheses in part (d) at a 0.5 level of significance. Present in the analysis of variance format

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check_circleAnswer
Step 1

a) Computation of mean square error:

Step-by-step procedure to obtain the mean square error using EXCEL software:

  • Create the variable time in first column and 2 indicator variables in second and third columns.
  • Select Data > Data Analysis > Regression.
  • Click OK.
  • Under Input Y Range enter $B$1:$B$6.
  • Under Input X Range enter $A$1:$A$6.
  • Check Labels.
  • Click OK.

Output using EXCEL software is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
0.919238816
0.845
Adjusted R Square
0.793333333
Standard Error
2.033060091
5
Observations
ANOVA
df
Significance F
SS
MS
F
Regression
Residual
1
67.6
67.6 16.35483871
0.027214829
12.4 4.133333333
Total
80
4
Coefficients Standard Error
Lower 95%
Upper 95%
Lower 95.0 %
Upper 95.0%
t Stat
P-value
Intercept
-1.4
2.727636339 -0.513264903 0.643173407 -10.08055619
7.28055619 -10.08055619
7.28055619
2.6
0.642910051 4.044111609 0.027214829
0.553973284 4.646026716 0.553973284 4.646026716
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SUMMARY OUTPUT Regression Statistics Multiple R R Square 0.919238816 0.845 Adjusted R Square 0.793333333 Standard Error 2.033060091 5 Observations ANOVA df Significance F SS MS F Regression Residual 1 67.6 67.6 16.35483871 0.027214829 12.4 4.133333333 Total 80 4 Coefficients Standard Error Lower 95% Upper 95% Lower 95.0 % Upper 95.0% t Stat P-value Intercept -1.4 2.727636339 -0.513264903 0.643173407 -10.08055619 7.28055619 -10.08055619 7.28055619 2.6 0.642910051 4.044111609 0.027214829 0.553973284 4.646026716 0.553973284 4.646026716

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Step 2

Mean square error:

From the ANOVA table in output, the mean square error of the regression is found to be 67.6.

Step 3

b) Standard error of the estimate:

Under regression statistics in the output, the standard ...

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