Only need B5 - B8! Thanks! The question below are to be answered after you have
ID: 3311589 • Letter: O
Question
Only need B5 - B8! Thanks!
The question below are to be answered after you have run a Multiple Regression model using the data set called Real Estate. The Model, postulates that the price of houses (y) is a linear function of 5 independent variables: Lot Size (x1), Age of the house (x2), Land Value (x3), Living Area (x4), and Number of the bedrooms (x5). Using our generic notations, we have:
y= f (x1, x2, x3, x4, x5).
The linear model specified is as follows:
y = o + 1x1 + 2x2 + 3x3 + 4x4 + 5x5 +
Answer the following questions about Multiple Regression.
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: 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? Calculate the value of the Durbin-Watson test statistics, using the formula from your Formula Sheet or look below:
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 x1 Residual P Regression Statistics 60 x2 Res Multiple R R Square Adjusted R Square Standard Error Observations 0.78330504 0.613566786 0.612444739 61283.64107 1728 60 20 20 20 -40 20 ANOVA MS Significance F S 20 Regression Residual Total 5 1.02686E+13 2.05371E+12 546.827741 17226.46729E+12 3755684663 17271.67359E+13 Coefficients Standard Error 41079.844416092.720777 6.742446587 2.11868E-11 6746.9460152139.790588 3.153087061 0.001643392 261.8781794 0.9592086180.046924459 20.44154878 2.51646E-83 92.405293433.578298102 25.823810871.4494E-124 6496.7342442454.477224-2.646891233 0.008197595 t Stat P-value Intercept x2 X3 52.4017967-4.997503824 6.39789E-07 Regression Equation Q:41079.84 + 6746.95*x1-261.88*x2 + 0.96"x3 +92.41*x4-6496.73*x5Explanation / Answer
B-1]
sample regression equation = 41079.84 + 6746.95*X1 - 261.88*X2 + 0.96*X3 + 92.41*X4 - 6496.73*X5
B-2]
At = 0.05, All Independent variables are significant except X5, because its corresponding P-value is 0.008 and is greater than the level of significance 0.005. Hence we accept null hypothesis, that is given indepedent variable is not significant.
B-3]
the overall significance of the model by conduction an F test.
F- test statistic is = 546.83 and P-value is near about zero, Hence at = 0.05 we reject null hypothesis
B-4]
the value of adjusted r-square = 0.6124
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