y 109000 155000 86060 120000 153000 170000 90000 122900 325000 120000 85860 97000 127000 89900 155000 253750 60000 87500 112000 104900 148635 150000 90400 248800 135000 145000 457000 140000 130000 187000 229000 227000 179900 169900 209900 169900 293000 24590 157000 195000 150000 234900 279550 246500 124000 138000 290000 108000 134900 64500 142000 125000 88000 135000 90000 90100 126900 175000 158000 92000 82800 140000 171000 200640 139000 225000 182000 208767 186000 93000 257386 161000 92000 211002 115000
x1 0.19 0.41 0.11 0.68 0.4 1.21 0.83 1.94 2.29 0.92 8.97 0.11 0.14 2 0.13 2 0.21 0.88 1 0.43 0.32 0.03 0.36 4 1.83 3 0.43 0.44 1.24 0.46 0.87 1.8 0.46 0.91 0.46 0.59 7.24 0.19 0.46 0.41 0.78 0.89 1.34 1 1 0.27 0.71 0.9 0.24 0.06 0.55 0.34 0.19 0.23 0.07 0.09 0.25 0.47 0.36 0.07 0.11 0.23 3.16 0.08 0.57 0.5 1 0.5 0.55 0.1 0.5 0.31 0.28 0.06 0.06
x2 133 13 20 31 33 23 36 4 123 1 13 153 9 88 9 7 82 17 12 21 1 24 16 28 126 26 53 56 51 3 9 201 1 19 1 10 43 2 45 32 54 9 60 70 98 54 73 48 10 16 20 32 15 135 14 15 10 15 10 14 225 25 15 4 30 12 16 8 17 14 90 10 18 12 14
x3 7300 18700 15000 14000 23300 14600 22200 21200 12600 22300 4800 3100 300 2500 300 49800 8500 19400 8600 5600 6200 5100 5200 5500 6000 4500 2700 19400 24800 15200 41100 25500 15200 20200 15200 17300 36600 20700 20200 27100 24500 41600 44400 17100 15500 8900 61000 19000 8000 1600 13800 11100 3400 8100 1800 2400 8400 27200 12100 1800 3900 8300 24100 32000 7500 15300 26600 32000 4400 2600 32000 10400 6300 32000 1600
x4 x5 Based on the Multiple Regression Output in Excel that you have created, using the data file provided to you, answer the following questions:
Note: In all Questions, where-ever needed, use the 0.05 level of significance to test the hypotheses (α = 0.05).
1.What is the Sample Regression Equation?
2. Which of the independent variables are significant? Why? Explain! Use α = 0.0.05 in ALL questions.
Use only the p-value to explain your answers (No need to go to tables).
3. Test the overall significance of the model by relying on F Statistic.
4. What is the value of adjusted r-square? Verify its value, using the related formula in your Formula Sheet for adjusted r-square and by using the values in your Excel Printout.
5. 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).
6. Do you see any Indication of Autocorrelation? Using Excel Formula commands, calculate the value of the Durbin-Watson test statistics in Excel, using the formula from your Formula Sheet or look below:
Durbin-Watson Test Statistics
(Also: Use the chart for Durbin Watson test provided in the Formula Sheet, or below). For Durbin-Watson TABLE, you can use your textbook or the Internet.
The Durbin–Watson Test for Autocorrelation
Autocorrelation
Test is inconclusive
No evidence of autocorrelation
Test is inconclusive
Autocorrelation
0
2
4-
4-
4
7. Do you see any evidence of Multicollinearity? Explain and provide evidence.
8. Has the Constant variance of the residual assumption (Homoscedasticity) been satisfied? Demonstrate and explain.