Question

Price (in K)	Sqft	Age	Features	CornerCODE	Corner_Label
310.0	2650	13	7	0	NO
313.0	2600	9	4	0	NO
320.0	2664	6	5	0	NO
320.0	2921	3	6	0	NO
304.9	2580	4	4	0	NO
295.0	2580	4	4	0	NO
285.0	2774	2	4	0	NO
261.0	1920	1	5	0	NO
250.0	2150	2	4	0	NO
249.9	1710	1	3	0	NO
242.5	1837	4	5	0	NO
232.0	1880	8	6	0	NO
230.0	2150	15	3	0	NO
228.5	1894	14	5	0	NO
222.0	1928	18	8	0	NO
223.0	1830	16	3	0	NO
220.5	1767	16	4	0	NO
216.0	1630	15	3	1	YES
218.9	1680	17	4	1	YES
204.5	1725	13	3	0	NO
204.5	1500	15	4	0	NO
202.5	1430	10	3	0	NO
202.5	1360	12	4	0	NO
195.0	1400	16	2	1	YES
201.0	1573	17	6	0	NO
191.0	1385	22	2	0	NO
274.5	2931	28	3	1	YES
260.3	2200	28	4	0	NO
230.0	2277	30	4	0	NO
235.0	2000	37	3	0	NO
207.0	1478	53	3	1	YES
207.0	1713	30	4	1	YES
197.2	1326	25	4	0	NO
197.5	1050	22	2	1	YES
194.9	1464	34	2	0	NO
190.0	1190	41	1	0	NO
192.6	1156	37	1	0	NO
194.0	1746	30	2	0	NO
192.0	1280	28	1	0	NO
175.0	1215	43	3	0	NO
177.0	1121	46	4	0	NO
177.0	1050	48	1	0	NO
179.9	1733	43	6	0	NO
178.1	1299	40	6	0	NO
177.5	1140	36	3	1	YES
172.0	1181	37	4	0	NO
320.0	2848	4	6	0	NO
264.9	2440	11	5	0	NO
240.0	2253	23	4	0	NO
234.9	2743	25	5	1	YES
230.0	2180	17	4	1	YES
228.9	1706	14	4	0	NO
225.0	1948	10	4	0	NO
217.5	1710	16	4	0	NO
215.0	1657	15	4	0	NO
213.0	2200	26	4	0	NO
210.0	1680	13	4	0	NO
209.9	1900	34	3	0	NO
200.5	1565	19	3	0	NO
198.4	1543	20	3	0	NO
192.5	1173	6	4	0	NO
193.9	1549	5	4	0	NO
190.5	1900	3	3	0	NO
188.5	1560	8	5	1	YES
186.0	1365	10	2	0	NO
185.5	1258	7	4	1	YES
184.9	1314	5	2	0	NO
180.0	1338	2	3	1	YES
180.9	997	4	4	0	NO
180.5	1275	8	5	0	NO
180.0	1030	4	1	0	NO
178.0	1027	5	3	0	NO
177.9	1007	19	6	0	NO
176.0	1083	22	4	0	NO
182.3	1320	18	5	0	NO
174.0	1348	15	2	0	NO
172.0	1350	12	2	0	NO
166.9	837	13	2	0	NO
234.5	3750	10	4	1	YES
202.5	1500	7	3	1	YES
198.9	1428	40	2	0	NO
187.0	1375	28	1	0	NO
183.0	1080	20	3	0	NO
182.0	900	23	3	0	NO
175.0	1505	16	2	1	YES
167.0	1480	19	4	0	NO
159.0	1142	10	0	0	NO
212.0	1464	7	2	0	NO
315.0	2116	25	3	0	NO
177.5	1280	14	3	0	NO
171.0	1159	23	0	0	NO
165.0	1198	10	4	0	NO
163.0	1051	15	2	0	NO
289.4	2250	40	6	0	NO
263.0	2563	17	2	0	NO
174.9	1400	45	1	1	YES
238.0	1850	5	5	1	YES
221.0	1720	5	4	0	NO
215.9	1740	4	3	0	NO
217.9	1700	6	4	0	NO
210.0	1620	6	4	0	NO
209.5	1630	6	4	0	NO
210.0	1920	8	4	0	NO
207.0	1606	5	4	0	NO
205.0	1535	7	5	1	YES
208.0	1540	6	2	1	YES
202.5	1739	13	3	0	NO
200.0	1715	8	3	0	NO
199.0	1305	5	3	0	NO
197.0	1415	7	4	0	NO
199.5	1580	9	3	0	NO
192.4	1236	3	4	0	NO
192.2	1229	6	3	0	NO
192.0	1273	4	4	0	NO
191.9	1165	7	4	0	NO
181.6	1200	7	4	1	YES
178.9	970	4	4	1	YES

Multiple Regression Modeling Steps

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

Answer:

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: