Question

Price (in K)	Sqft
310.0	2650
313.0	2600
320.0	2664
320.0	2921
304.9	2580
295.0	2580
285.0	2774
261.0	1920
250.0	2150
249.9	1710
242.5	1837
232.0	1880
230.0	2150
228.5	1894
222.0	1928
223.0	1830
220.5	1767
216.0	1630
218.9	1680
204.5	1725
204.5	1500
202.5	1430
202.5	1360
195.0	1400
201.0	1573
191.0	1385
274.5	2931
260.3	2200
230.0	2277
235.0	2000
207.0	1478
207.0	1713
197.2	1326
197.5	1050
194.9	1464
190.0	1190
192.6	1156
194.0	1746
192.0	1280
175.0	1215
177.0	1121
177.0	1050
179.9	1733
178.1	1299
177.5	1140
172.0	1181
320.0	2848
264.9	2440
240.0	2253
234.9	2743
230.0	2180
228.9	1706
225.0	1948
217.5	1710
215.0	1657
213.0	2200
210.0	1680
209.9	1900
200.5	1565
198.4	1543
192.5	1173
193.9	1549
190.5	1900
188.5	1560
186.0	1365
185.5	1258
184.9	1314
180.0	1338
180.9	997
180.5	1275
180.0	1030
178.0	1027
177.9	1007
176.0	1083
182.3	1320
174.0	1348
172.0	1350
166.9	837
234.5	3750
202.5	1500
198.9	1428
187.0	1375
183.0	1080
182.0	900
175.0	1505
167.0	1480
159.0	1142
212.0	1464
315.0	2116
177.5	1280
171.0	1159
165.0	1198
163.0	1051
289.4	2250
263.0	2563
174.9	1400
238.0	1850
221.0	1720
215.9	1740
217.9	1700
210.0	1620
209.5	1630
210.0	1920
207.0	1606
205.0	1535
208.0	1540
202.5	1739
200.0	1715
199.0	1305
197.0	1415
199.5	1580
192.4	1236
192.2	1229
192.0	1273
191.9	1165
181.6	1200
178.9	970

1. Open the Excel worksheet containing your Team Project Data.
2. As you learned in Modules 3 and 4, you will be using the set of potentially meaningful numerical independent variables and the one selected “two-category” dummy variable in your study to develop a “best” multiple regression model for predicting your numerical response variable Y. Follow the step by step modeling process described in the PowerPoints at the end of Module 4.
   1. Start with a visual assessment of the possible relationships of your numerical dependent variable Y with each potential predictor variable by developing the scatterplot matrix (use JMP) and paste this into your report.
   2. Then fit a preliminary multiple regression model using these potential numerical predictor variables and, at most, one categorical dummy variable.
   3. Then assess collinearity with VIF until you are satisfied that you have a final set of possible predictors that are “independent,” i.e., not unduly correlated with each other.
   4. Use stepwise regression approaches to fit a multiple regression model with this set of potentially meaningful numerical independent variables (and, if appropriate, the one selected categorical dummy variable).
      1. (1) Based on the forward modeling criterion determine which independent variables should be included in your regression model.
      2. (2) Based on the backward selection modeling criterion determine which independent variables should be included in your regression model.
      3. (3) Based on the mixed selection modeling criterion determine which independent variables should be included in your regression model.
      4. (4) Based on the Adjusted r² criterion determine which independent variables should be included in your regression model.
   5. Comment on the consistency of your findings in Step 2D (1)-(4).
   6. Paste screenshots of (1), (2), and (3) outputs from Step 2D above into your report.
   7. Based on Step 2D (along with the principle of parsimony if necessary) select a “best”multiple regression model.
   8. Using the predictor variables from your selected “best” multiple regression model, rerun the multiple regression model in order to assess its assumptions. You may use Excel or JMP for this step.
   9. Look at the set of residual plots, cut and paste them into the report, and briefly comment on the appropriateness of your fitted model.
      1. (1) If the assumptions are met and the fitted model is appropriate, continue to Step 2J.
      2. (2) If the normality assumption is problematic, state this but continue to Step 2J with caution because your sample size is large enough for the central limit theorem to enable the use of classical inferential methods. Note: You do not need to check the assumption of independence in your project. That assumption is met because your project is not time-dependent.
      3. (3) If either the linearity or equality of variance assumption is violated in one or two scatter plots of Y with individual predictors then transform the particular independent variables involved following Tukey’s “ladder of powers” and rerun the multiple regression model as in Step 2H.
   10. Assess the significance of the overall fitted model.
   11. Assess the significance of each predictor variable.
3. Write the sample multiple regression equation for the “final best” model you have developed.
   1. Interpret the meaning of the Y intercept and interpret the meaning of all the slopes for your fitted model (but do this in whatever units you used for Y to build this model).
   2. Interpret the meaning of the coefficient of multiple determination r ² .
   3. Interpret the meaning of the standard error of the estimate SYX (in the units you used to build this model).
   4. Determine the 95% confidence interval estimate of the average value of Y for all occasions when the independent variables have the values you selected.
   5. Select one value for each of your independent variables in their respective relevant ranges:
   6. Predict ŷ

Answer 1

1. 1. 1. 2) If the normality assumption is problematic, state this but continue to Step 2J with caution because your sample size is large enough for the central limit theorem to enable the use of classical inferential methods. Note: You do not need to check the assumption of independence in your project. That assumption is met because your project is not time-dependent.
      2. (3) If either the linearity or equality of variance assumption is violated in one or two scatter plots of Y with individual predictors then transform the particular independent variables involved following Tukey’s “ladder of powers” and rerun the multiple regression model as in Step 2H.
   2. Assess the significance of the overall fitted model.
   3. Assess the significance of each predictor variable.
2. Write the sample multiple regression equation for the “final best” model you have developed.
   1. Interpret the meaning of the Y intercept and interpret the meaning of all the slopes for your fitted model (but do this in whatever units you used for Y to build this model).
   2. Interpret the meaning of the coefficient of multiple determination r2 .
   3. Interpret the meaning of the standard error of the estimate SYX (in the units you used to build this model).
   4. Determine the 95% confidence interval estimate of the average value of Y for all occasions when the independent variables have the values you selected.
   5. Select one value for each of your independent variables in their respective relevant ranges: