# Stats

posted by
**Kim**
.

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 ¡Ý 10) or at least Doane¡¯s Rule (n/k ¡Ý 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 ¦Á = .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 ¦Á = .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

Floor Office Entrance

Obs Assess Flo Offic Entran Age Freeway

1 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