Instructions for Data Sets: In each data set, the dependent variable (response) is the first variable. Choose the independent variables (predictors) as you judge appropriate. Use a spreadsheet or a statistical package (e.g., MegaStat or MINITAB) to perform the necessary regression calculations and to obtain the required graphs. Write a concise report answering questions 13.9 through 13.25. Label sections of your report to correspond to the questions. Insert tables and graphs in your report as appropriate.
13.9 Is this cross-sectional data or time-series data? What is the unit of observation (e.g., firm, individual, year)?
13.10 Are the X and Y data well-conditioned? If not, make any transformations that may be necessary and explain.
13.11 State your a priori hypotheses about the sign (+ or −) of each predictor and your reasoning about cause and effect. Would the intercept have meaning in this problem? Explain.
13.12 Does your sample size fulfill Evans’s Rule (n/k ≥ 10) or at least Doane’s Rule (n/k ≥ 5)?
13.13 Perform the regression and write the estimated regression equation (round off to 3 or 4 significant digits for clarity). Do the coefficient signs agree with your a priori expectations?
13.14 Does the 95 percent confidence interval for each predictor coefficient include zero? What conclusion can you draw? Note: Skip this question if you are using MINITAB, since predictor confidence intervals are not shown.
13.15 Do a two-tailed t test for zero slope for each predictor coefficient at α = .05. State the degrees of freedom and look up the critical value in Appendix D (or from Excel).
13.16 (a) Which p-values indicate predictor significance at α = .05? (b) Do the p-values support the conclusions you reached from the t tests? (c) Do you prefer the t test or the p-value approach? Why?
13.17 Based on the R2 and ANOVA table for your model, how would you describe the fit?
13.18 Use the standard error to construct an approximate prediction interval for Y. Based on the width of this prediction interval, would you say the predictions are good enough to have practical value?
13.19 (a) Generate a correlation matrix for your predictors. Round the results to three decimal places. (b) Based on the correlation matrix, is collinearity a problem? What rules of thumb (if any) are you using?
13.20 (a) If you did not already do so, re-run the regression requesting variance inflation factors (VIFs) for your predictors. (b) Do the VIFs suggest that multicollinearity is a problem? Explain.
13.21 (a) If you did not already do so, request a table of standardized residuals. (b) Are any residuals outliers (three standard errors) or unusual (two standard errors)?
13.22 If you did not already do so, request leverage statistics. Are any observations influential? Explain.
13.23 If you did not already do so, request a histogram of standardized residuals and/or a normal probability plot. Do the residuals suggest non-normal errors? Explain.
13.24 If you did not already do so, request a plot of residuals versus the fitted Y. Is heteroscedasticity a concern?
13.25 If you are using time-series data, perform one or more tests for autocorrelation (visual inspection of residuals plotted against observation order, runs test, Durbin-Watson test). Is autocorrelation a concern?
DATA SET C Assessed Value of Small Medical Office Buildings (n = 32, k = 5)
Assessed
Obs Assessed Floor Offices Entrances Age Freeway
Obs / Assessed / Floor / Offices / Entrances / Age / Freeway1 / 1796 / 4790 / 4 / 2 / 8 / 0
2 / 1544 / 4720 / 3 / 2 / 12 / 0
3 / 2094 / 5940 / 4 / 2 / 2 / 0
4 / 1968 / 5720 / 4 / 2 / 34 / 1
5 / 1567 / 3660 / 3 / 2 / 38 / 1
6 / 1878 / 5000 / 4 / 2 / 31 / 1
7 / 949 / 2990 / 2 / 1 / 19 / 0
8 / 910 / 2610 / 2 / 1 / 48 / 0
9 / 1774 / 5650 / 4 / 2 / 42 / 0
10 / 1187 / 3570 / 2 / 1 / 4 / 1
11 / 1113 / 2930 / 3 / 2 / 15 / 1
12 / 671 / 1280 / 2 / 1 / 31 / 1
13 / 1678 / 4880 / 3 / 2 / 42 / 1
14 / 710 / 1620 / 1 / 2 / 35 / 1
15 / 678 / 1820 / 2 / 1 / 17 / 1
16 / 1585 / 4530 / 2 / 2 / 5 / 1
17 / 842 / 2570 / 2 / 1 / 13 / 0
18 / 1539 / 4690 / 2 / 2 / 45 / 0
19 / 433 / 1280 / 1 / 1 / 45 / 1
20 / 1268 / 4100 / 3 / 1 / 27 / 0
21 / 1251 / 3530 / 2 / 2 / 41 / 1
22 / 1094 / 3660 / 2 / 2 / 33 / 0
23 / 638 / 1110 / 1 / 2 / 50 / 1
24 / 999 / 2670 / 2 / 2 / 39 / 1
25 / 653 / 1100 / 1 / 1 / 20 / 1
26 / 1914 / 5810 / 4 / 3 / 17 / 0
27 / 772 / 2560 / 2 / 2 / 24 / 0
28 / 890 / 2340 / 3 / 1 / 5 / 0
29 / 1282 / 3690 / 2 / 2 / 15 / 1
30 / 1264 / 3580 / 3 / 2 / 27 / 0
31 / 1162 / 3610 / 2 / 1 / 8 / 1
32 / 1447 / 3960 / 3 / 2 / 17 / 0
Assessed = assessed value (thousands of dollars), Floor = square feet of floor space, Offices = number of offices in the building, Entrances = number of customer entrances (excluding service doors), Age = age of the building (years), Freeway = 1 if within one mile of freeway, 0 otherwise