Price (in K) Sqft Age Features CornerCODE Corner_Label 310.0 2650 13 7 0 NO 313.0 2600 9 4 0 ...
| 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
- Open the Excel worksheet containing your Team Project Data.
- 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.
- 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.
- Then fit a preliminary multiple regression model using these potential numerical predictor variables and, at most, one categorical dummy variable.
- 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.
- 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) Based on the forward modeling criterion determine which independent variables should be included in your regression model.
- (2) Based on the backward selection modeling criterion determine which independent variables should be included in your regression model.
- (3) Based on the mixed selection modeling criterion determine which independent variables should be included in your regression model.
- (4) Based on the Adjusted r2 criterion determine which independent variables should be included in your regression model.
- Comment on the consistency of your findings in Step 2D (1)-(4).
- Paste screenshots of (1), (2), and (3) outputs from Step 2D above into your report.
- Based on Step 2D (along with the principle of parsimony if necessary) select a “best”multiple regression model.
- 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.
- 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) If the assumptions are met and the fitted model is appropriate, continue to Step 2J.
- (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) 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.
- Assess the significance of the overall fitted model.
- Assess the significance of each predictor variable.
- Write the sample multiple regression equation for the “final
best” model you have developed.
- 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).
- Interpret the meaning of the coefficient of multiple determination r 2 .
- Interpret the meaning of the standard error of the estimate SYX (in the units you used to build this model).
- Determine the 95% confidence interval estimate of the average value of Y for all occasions when the independent variables have the values you selected.
- Select one value for each of your independent variables in their respective relevant ranges:
- Predict ŷ
Homework Answers
Answer:
-
-
- 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) 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.
- Assess the significance of the overall fitted model.
- Assess the significance of each predictor variable.
-
- Write the sample multiple
regression equation for the “final best” model you have developed.
- 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).
- Interpret the meaning of the coefficient of multiple determination r2 .
- Interpret the meaning of the standard error of the estimate SYX (in the units you used to build this model).
- Determine the 95% confidence interval estimate of the average value of Y for all occasions when the independent variables have the values you selected.
- Select one value for each of your independent variables in their respective relevant ranges:
Add Answer to:
Price (in K) Sqft Age Features CornerCODE Corner_Label 310.0 2650 13 7 0 NO 313.0 2600 9 4 0 ...
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Age Mem IQ Reading Ability 6.7 4.4 95 7.2 5.9 4 90 6 5.5 4.1 105 6 6.2 4.8 98 6.6 6.4 5 ...
Age Mem
IQ Reading
Ability
6.7
4.4
95 7.2
5.9
4
90 6
5.5
4.1
105 6
6.2
4.8
98 6.6
6.4
5
106 7
7.3
5.5
100 7.2
5.7
3.6
88 5.3
6.15
5
95 6.4
7.5
5.4
96 6.6
6.9
5
104 7.3
4.1
3.9
108 5
5.5
4.2
90 5.8
6.9
4.5
91 6.6
7.2
5
92 6.8
4
4.2
101 5.6
7.3
5.5
100 7.2
5.9
4
90 6
5.5
4.2
90 5.8
4
4.2
101 ...
Question 1 : Is the magnitude of an earthquake related to the depth below the surface...
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3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider...
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Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% con...
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Conc Ratio Temp Time Rating 2 4 180 7 2.25 2 4 100 3 1.6 2...
Conc Ratio Temp Time Rating 2 4 180 7 2.25 2 4 100 3 1.6 2 13 140 1 3.1 4 7 140 3 4.8 4 10 180 3 4.5 4 10 160 5 4.6 4 13 100 7 4.3 4 1 180 7 1.8 4 1 100 1 1.3 4 1 100 1 1.4 4 1 100 1 1.45 5 4 160 7 4.5 5 1 100 7 1.4 5 4 100 1 1.7 5 13 140 1 4.5...
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1. (4pt) A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called a. a constant variable b. a dummy variable c. an interaction d. None of these alternatives are correct. 2. (4pt) The model y = Bo + B1X1 + B2X2 +E is called a. First-order model with one predictor variable b. First-order model with two predictor variables c. Second-order model with two...
Age Mem
IQ Reading
Ability
6.7
4.4
95 7.2
5.9
4
90 6
5.5
4.1
105 6
6.2
4.8
98 6.6
6.4
5
106 7
7.3
5.5
100 7.2
5.7
3.6
88 5.3
6.15
5
95 6.4
7.5
5.4
96 6.6
6.9
5
104 7.3
4.1
3.9
108 5
5.5
4.2
90 5.8
6.9
4.5
91 6.6
7.2
5
92 6.8
4
4.2
101 5.6
7.3
5.5
100 7.2
5.9
4
90 6
5.5
4.2
90 5.8
4
4.2
101 ...
Question 1 : Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? In order to answer this question an analysis is conducted. Let we wish to explain depth (in kilometers) of the quake below the surface at the epicenterx by magnitude of an earthquake (on the Richter scale). Data are as follows: 1 2 3 4 5 6 7 8 9 10 3.9 4.3 3.3 4.6 3.9 3.2 3.4 4.5 5.1...
3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider a problem of regressing y on two (qualitative) variables r, 2. Data: 22 obs no. y (Income) 2 (Management Status) I (Gender) 1 None Female 2 None Male Yes Female Yes Male 4 To handle the qualitative variables r, 12, we define dummy variables 1, 22 as for 1, 22= Yes Male for 1, 219 22 -1. for 22= None for 1= Female -1,...
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