Question
Asked Sep 11, 2019
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Question 3:
From the data below;
x1 1 2 3 4 5
y1 3 7 5 11 14

a) Compute the mean square error
b) Compute the standard error of the estimate
c) Compute the estimated standard deviation of b1
d) Use the t-test to test the following hypothesis (α= .05)
Ho: β1 = 0
Ha: β1 ≠ 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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Expert Answer

Step 1

(a)

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 $A$1:$A$6.
  • Under Input X Range enter $B$1:$C$6.
  • Click the box of Labels.
  • Under...
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SUMMARY OUTPUT Regression Statistics Multiple R R Square 0.919238816 0.845 0.793333333 Adjusted R Square Standard Error 2.033060091 Observations ANOVA Significance F 67.6 16.35483871 0.027214829 df SS MS Regression 1 67.6 3 Residual 12.4 4.133333333 Total 4 80 Lower 95.0 % Lower 95% Coefficients Standard Error Upper 95% Upper 95.0 % t Stat P-value 0.2 2.132291412 0.09379581 0.931184657 -6.585902927 6.985902927 -6.585902927 6.985902927 Intercept X1 2.6 0.642910051 4.044111609 0.027214829 0.553973284 4.646026716 0.553973284 4.646026716

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