Note: In all Questions, where-ever needed, use the 5% level of significance to t
ID: 3316445 • Letter: N
Question
Note: In all Questions, where-ever needed, use the 5% level of significance to test the hypotheses ( = 0.05).
B1.What is the Sample Regression Equation?
B2. Which of the Independent variables are significant? Why? Explain. Use = 0.05 in ALL questions.
Use only the p-value to explain your answers (No need to go to tables).
B3. Test the overall significance of the model by conduction an F test.
B4. What is the value of adjusted r-square? Verify its value, using the formula for adjusted r-square and using the values in your Excel Printout.
B5. Comment on the Normality assumption for the residuals for this model. In other word, has the normality assumption been satisfied? Explain your answer (Hint: you need to run Excel’s Histogram feature for Column of the Residuals).
B6. Do you see any indication of Multicollinearity? Explain why. (Hint: In addition to indications you can detect from Excel Output, run the Correlation Matrix of the Independent Variables). Can you find any evidence of Multicollinearity without referring to the Correlation Matrix? Explain.
B7. Do you see any Indication of Autocorrelation? Using Excel Formula commands, calculate the value of the Durbin-Watson test statistics, using the formula from your Formula Sheet
B8. Do you see any indication of Heteroscedasticity for the Variable X3? Copy and paste the residuals for this variable only. Demonstrate and Explain why.
SUMMARY OUTPUT Regression Statistics Multiple R Square Adjusted R Square0.38403506 Standard Error Observations 0.62961597 0.39641627 0.13904604 200 ANOVA MS Significance Regression Residual Total 4 2.476086382 0.619021596 32.0176 1.66019E-20 195 3.770091139 0.019333801 199 6.246177522 Coefficients Standard Error P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 4.87654342 0.045955234 106.1150811 2E-174 4.785910319 4.967176518 4.785910319 4.967176518 0.03090035 0.01011244 3.055677135 0.00256 0.010956557 0.050844148 0.010956557 0.050844148 -0.001106 0.000265702-4.16255713 4.7E-05-0.001630018 -0.00058198-0.00163002-0.00058198 0.00134664 0.000190878 7.05498762 2.9E-110.000970191 0.001723092 0.000970191 0.001723092 0.000248377.96537E-053.11809977 0.0021 9.12749E-05 0.000405462 9.12749E-05 0.000405462 t Stat Intercept x2Explanation / Answer
1) from the given excel ouput
sample regression equation
Y = 4.8765 + 0.031x1 -0.001x2 + 0.00135x3 + 0.00025x6
2) Decision rule : if p value < 0.05, then variable is significant
Actual decision : all the variables are significant, since all p values are < 0.05
3) F test
Decision rule : if F statistic > F critical , then regression model is fit for prediction
Actual decision : F statistic = 32.0176 > 1.66
then regression model is fit
4) Adjusted r square = 0.384
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