07 Jun COMM 291 ASSIGNMENT 6 Two Questions Solution
Question
Question 1 – Office Rents
An economist wanted to investigate the relationship between office rents and vacancy rates. He took a random sample of monthly office rents (Rent), the percentage of vacant office space (Vacancy)and the city’s unemployment rate (Unemployment) in 30 different cities. The data are in the worksheet OfficeRents in the Excel spreadsheet.
- a) Fit a regression model to predictRentfrom Vacancy and Unemployment.
- a) Compute and interpret the value of R-squared.
- a) What would your conclusion be if you test the hypothesis that the coefficients forVacancyandUnemploymentare both zero? Explain in one sentence. Include the test-statistic, the degrees of freedom and the P-value in your answer.
- a) What would your conclusion be from a hypothesis test for the coefficient forVacancy? Explain in one sentence. Include the corresponding test-statistic, degrees of freedom and P-value in your answer.
- a) Examine the distribution of the residuals and plot the residuals versus each of the explanatory variables. Describe your findings. Does your analysis suggest that the model assumptions may not be reasonable for this problem? Explain.
- f) Fit a regression model to predictRentusing onlyVacancy. Explain why the coefficient for years in rank and the results of a significance test for this coefficient differ from what you found in parts (a) and (d) above.
<pclass=”msonormal” style=”box-sizing: border-box;”>g) Give an approximate 95% prediction interval for the office rent in a city whose vacancy rate is 10% and whose unemployment rate is 7%.</pclass=”msonormal”>
Question 2 – Simple Linear Regression MS Excel Template
Below is the template for the output from simple regression using MS Excel. But instead of actual results, the cells are numbered from (1) to (27). Your task is to provide the formulas used to compute each of the cell entries. You can answer this in neat handwritten form; you do not need to type the formulas! Just write each cell number and the corresponding formula after it.
Some of these statistics can be obtained by more than one formula. Any correct formula is acceptable. Some of these are most easily obtained from other cells in the table. If so, use “Cell X” as part of your formula.
Note: This will be excellent practice for the final exam. We suggest that you keep a copy of your answers to this question as a formula sheet for the exam.
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | (1) | |||||
| R Square | (2) | |||||
| Adjusted R Square | (3) | |||||
| Standard Error | (4) | |||||
| Observations | (5) | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | (6) | (7) | (8) | (9) | (10) | |
| Residual | (11) | (12) | (13) | |||
| Total | (14) | (15) | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | (16) | (17) | (18) | (19) | (20) | (21) |
| X Variable | (22) | (23) | (24) | (25) | (26) | (27) |
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