AGEC 440 Homework #3 100 Points Available This Homework Will Use the Homework 3 Excel Data Sheet (Data Tab) Please carry any decimals out two places if numbers are involved in your answer. 1. Previously you were assigned the task of determining correlation coefficients for some real estate data. The agent that hired you was impressed with your work and wanted you to perform further analysis with the data. The agent is interested in finding out some answers for several questions and you will need to use econometrics to answer those questions. She mainly wants to help her clients price their home accurately with respect to how the market values certain home criteria. The agent also added a new field to the data, SELL PRICE which was the actual sales price of the listed homes. Data Descriptions: Note that the values for Pool, Fireplace and Waterfront indicate the presence of these amenities. For example, if the home has a Fireplace, the value is set to 1, otherwise it is 0. The same interpretation is applied for Pool and Waterfront. (a) Compute a Correlation Analysis for all variables but only report the correlation metrics with respect to Sell Price (do not include List Price) using the option under Excel's Data Analysis for all the variables supplied under the Data tab. (6 Points) (b) Run a multiple regression using Sell Price as the dependent variable and all the other remaining variables with the exception of List Price as the independent variables. You will use the output from this procedure to answer the remaining questions. i. Evaluate the F-test for the regression. Use an alpha (or level of significance) of 0.05 to assess whether the Mean Squares (MS) are statistically different between the Regression and the Residuals. Is the F-test metric significant? (3 Points) ii. Comment on the significance of the coefficients estimated from the regression. Recall the null hypothesis in the individual coefficient t- test of B-O and the alternative hypothesis B not equal to 0. Use an alpha (or level of significance) of 0.05. (6 Points) iii. Describe what the Coefficient of Determination means for this model (the R2). (6 Points) iv. You discuss the results with the agent and conclude that the coefficient for Bedrooms should not be negative as the agent feels that many home buyers would pay more to have more bedrooms in a home. Indeed, the correlation coefficient of Bedrooms with respect to Sell Price is positive. The agent starts to panic, but you recall from AGEC 440 that sometimes multicollinearity occurs when data measuring similar characteristics are included in the same regression. In order to investigate this, run a correlation analysis of all variables (except List Price) with respect to Bedrooms and place your output below. Which variable has the strongest correlation (+ or -) with respect to Bedrooms? (8 Points) 2. You conclude that in order to handle the collinearity issue you will take a practical approach of dropping either SQFT or Bedrooms from the analysis. Run a multiple regression using Sell Price as the dependent variable and all the other remaining variables with the exception of List Price and SQFT as the independent variables. You will use the output from this procedure to answer the remaining questions. i. Evaluate the F-test for the regression. Use an alpha (or level of significance) of 0.05 to assess whether the Mean Squares (MS) are statistically different between the Regression and the Residuals. Is the F-test metric significant? (5 Points) ii. Comment on the significance of the coefficients estimated from the regression. Recall the null hypothesis in the individual coefficient t- test of B = 0 and the alternative hypothesis B not equal to 0. Use an alpha (or level of significance) of 0.05. (10 Points) iii. Describe what the Coefficient of Determination means for this model (the R2). (6 Points) a 3. Now run a multiple regression using Sell Price as the dependent variable and all the other remaining variables with the exception of List Price and Bedrooms as the independent variables. You will use the output from this procedure to answer the remaining questions. 1. Evaluate the F-test for the regression. Use an alpha (or level of significance) of 0.05 to assess whether the Mean Squares (MS) are statistically different between the Regression and the Residuals. Is the F-test metric significant? (5 Points) ii. Comment on the significance of the coefficients estimated from the regression. Recall the null hypothesis in the individual coefficient t- test of B = 0 and the alternative hypothesis B not equal to 0. Use an alpha (or level of significance) of 0.05. (10 Points) iii. Describe what the Coefficient of Determination means for this model (the R2). (6 Points) 4. Of the models you estimated in numbers 2. and 3. above which model do you think does the "best" job of explaining variation in Sell Price? Explain your answer if you want full credit. (8 Points) 5. The following questions pertain to the model you estimated in number 3: 1. Write the regression equation for the model you estimated in number 3. Be careful to not use any coefficient that is not statistically different from 0. (8 Points) ii. Using your regression equation, predict the Sell Price when SQFT = 2,800, Bathrooms - 3, and the Home Age = 6. (8 Points) it. The realtor has clients that are considering buying a home with a Waterfront and they want to know how much a home lot with a Waterfront contributes to the selling price. What would you tell them? (5 Points) Real Estate Data SQFT 741 741 POOL 1 1 0 0 0 790 190 FIREPLACE 1 0 1 1 0 1 1 1 1 1 1 0 1 D 0 0 2783 1165 2331 1228 1228 1228 1228 1228 1520 1440 1001 1438 956 1080 1745 971 1303 1590 0 0 0 O 0 0 0 0 0 D 933 890 LIST PRICE 66500 66000 68500 102000 54000 143000 98900 98350 98847 98900 101313 125000 62500 92000 120000 23000 22654 95000 64900 75000 68000 23000 40101 93000 58500 103500 102565 97900 99000 82000 171500 135900 80001 136000 167500 134000 270000 315000 207000 197500 335000 219000 189900 79900 123400 123000 130500 128000 68000 62000 124000 S0000 89900 SELL PRICE 63991 63509 65915 96416 51962 136927 93486 92966 93436 93486 95767 119457 60142 84307 114679 22132 21799 87056 62451 68729 65434 22132 38588 85224 56292 97834 96950 92540 93580 75143 160145 131843 73311 131940 156410 130000 260896 304379 189561 180861 323705 200550 173901 73219 117928 117546 126604 122324 65434 59660 118501 48133 82383 BEDROOMS BATHROOMS HOME AGE 1 18 1 1 18 1 1 18 2 2 18 2 1 35 2 2 25 2 2 25 2 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GOOOOOOOOO o o o od 1 13 18 D 1 4 ug 164000 295000 152000 195900 202500 152000 149000 195000 172600 122570 185000 1280000 123808 374000 1 1 0 1 0 153142 285053 145545 179396 185440 145545 142673 178572 161172 117135 169414 1236842 118318 361390 2456 3729 1588 4000 2650 3143 2967 4110 4 4 4 4 4 4 4 4 5 5 5 5 7 2 3 2 3 3 2 3 2 3 3 3 3 8 5 8 8 25 13 25 13 25 13 13 25 25 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 57 42 47 0 77 72 78 62 32 48 34 293 4 13 28 mmmona *u 3594 2853 4599 7086 3148 6203 1 1 1 1 1 1 4 1 oron 1 4 AGEC 440 Homework #3 100 Points Available This Homework Will Use the Homework 3 Excel Data Sheet (Data Tab) Please carry any decimals out two places if numbers are involved in your answer. 1. Previously you were assigned the task of determining correlation coefficients for some real estate data. The agent that hired you was impressed with your work and wanted you to perform further analysis with the data. The agent is interested in finding out some answers for several questions and you will need to use econometrics to answer those questions. She mainly wants to help her clients price their home accurately with respect to how the market values certain home criteria. The agent also added a new field to the data, SELL PRICE which was the actual sales price of the listed homes. Data Descriptions: Note that the values for Pool, Fireplace and Waterfront indicate the presence of these amenities. For example, if the home has a Fireplace, the value is set to 1, otherwise it is 0. The same interpretation is applied for Pool and Waterfront. (a) Compute a Correlation Analysis for all variables but only report the correlation metrics with respect to Sell Price (do not include List Price) using the option under Excel's Data Analysis for all the variables supplied under the Data tab. (6 Points) (b) Run a multiple regression using Sell Price as the dependent variable and all the other remaining variables with the exception of List Price as the independent variables. You will use the output from this procedure to answer the remaining questions. i. Evaluate the F-test for the regression. Use an alpha (or level of significance) of 0.05 to assess whether the Mean Squares (MS) are statistically different between the Regression and the Residuals. Is the F-test metric significant? (3 Points) ii. Comment on the significance of the coefficients estimated from the regression. Recall the null hypothesis in the individual coefficient t- test of B-O and the alternative hypothesis B not equal to 0. Use an alpha (or level of significance) of 0.05. (6 Points) iii. Describe what the Coefficient of Determination means for this model (the R2). (6 Points) iv. You discuss the results with the agent and conclude that the coefficient for Bedrooms should not be negative as the agent feels that many home buyers would pay more to have more bedrooms in a home. Indeed, the correlation coefficient of Bedrooms with respect to Sell Price is positive. The agent starts to panic, but you recall from AGEC 440 that sometimes multicollinearity occurs when data measuring similar characteristics are included in the same regression. In order to investigate this, run a correlation analysis of all variables (except List Price) with respect to Bedrooms and place your output below. Which variable has the strongest correlation (+ or -) with respect to Bedrooms? (8 Points) 2. You conclude that in order to handle the collinearity issue you will take a practical approach of dropping either SQFT or Bedrooms from the analysis. Run a multiple regression using Sell Price as the dependent variable and all the other remaining variables with the exception of List Price and SQFT as the independent variables. You will use the output from this procedure to answer the remaining questions. i. Evaluate the F-test for the regression. Use an alpha (or level of significance) of 0.05 to assess whether the Mean Squares (MS) are statistically different between the Regression and the Residuals. Is the F-test metric significant? (5 Points) ii. Comment on the significance of the coefficients estimated from the regression. Recall the null hypothesis in the individual coefficient t- test of B = 0 and the alternative hypothesis B not equal to 0. Use an alpha (or level of significance) of 0.05. (10 Points) iii. Describe what the Coefficient of Determination means for this model (the R2). (6 Points) a 3. Now run a multiple regression using Sell Price as the dependent variable and all the other remaining variables with the exception of List Price and Bedrooms as the independent variables. You will use the output from this procedure to answer the remaining questions. 1. Evaluate the F-test for the regression. Use an alpha (or level of significance) of 0.05 to assess whether the Mean Squares (MS) are statistically different between the Regression and the Residuals. Is the F-test metric significant? (5 Points) ii. Comment on the significance of the coefficients estimated from the regression. Recall the null hypothesis in the individual coefficient t- test of B = 0 and the alternative hypothesis B not equal to 0. Use an alpha (or level of significance) of 0.05. (10 Points) iii. Describe what the Coefficient of Determination means for this model (the R2). (6 Points) 4. Of the models you estimated in numbers 2. and 3. above which model do you think does the "best" job of explaining variation in Sell Price? Explain your answer if you want full credit. (8 Points) 5. The following questions pertain to the model you estimated in number 3: 1. Write the regression equation for the model you estimated in number 3. Be careful to not use any coefficient that is not statistically different from 0. (8 Points) ii. Using your regression equation, predict the Sell Price when SQFT = 2,800, Bathrooms - 3, and the Home Age = 6. (8 Points) it. The realtor has clients that are considering buying a home with a Waterfront and they want to know how much a home lot with a Waterfront contributes to the selling price. What would you tell them? (5 Points) Real Estate Data SQFT 741 741 POOL 1 1 0 0 0 790 190 FIREPLACE 1 0 1 1 0 1 1 1 1 1 1 0 1 D 0 0 2783 1165 2331 1228 1228 1228 1228 1228 1520 1440 1001 1438 956 1080 1745 971 1303 1590 0 0 0 O 0 0 0 0 0 D 933 890 LIST PRICE 66500 66000 68500 102000 54000 143000 98900 98350 98847 98900 101313 125000 62500 92000 120000 23000 22654 95000 64900 75000 68000 23000 40101 93000 58500 103500 102565 97900 99000 82000 171500 135900 80001 136000 167500 134000 270000 315000 207000 197500 335000 219000 189900 79900 123400 123000 130500 128000 68000 62000 124000 S0000 89900 SELL PRICE 63991 63509 65915 96416 51962 136927 93486 92966 93436 93486 95767 119457 60142 84307 114679 22132 21799 87056 62451 68729 65434 22132 38588 85224 56292 97834 96950 92540 93580 75143 160145 131843 73311 131940 156410 130000 260896 304379 189561 180861 323705 200550 173901 73219 117928 117546 126604 122324 65434 59660 118501 48133 82383 BEDROOMS BATHROOMS HOME AGE 1 18 1 1 18 1 1 18 2 2 18 2 1 35 2 2 25 2 2 25 2 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