SUMMARY OUTPUT Regression Statistics Multiple R 0.05860241 R Square 0.00343424 Adjusted RS -2.191E-06 Standard Err 660937.324 Observations 292 ANOVA df Regression Residual Total SS MS F Significance F 1 4.3656E+11 4.3656E+11 0.99936248 0.31829822 290 1.2668E+14 4.3684E+11 291 1.2712E+14 Coefficients tandard Erroi t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 917880.048 63923.8614 14.3589581 1.0941E-35 792066.517 1043693.58 792066.517 1043693.58 566000 0.26328107 0.26336503 0.99968119 0.31829822 -0.2550682 0.78163031 -0.2550682 0.78163031 Milestone 3 - Model development of property prices Belle also recently heard in the media that the proportion of sales are as follows: . . . 35% of sales are apartments; 45% of sales are houses; 10% of sales are townhouses; 5% of sales are villas and; 5% of sales are other. Belle would like to know if the sample data is statistically different to what the media is suggesting. Remember to state your assumptions and limitations of the result. In addition to this, Belle would like you to develop a propriety model to predict Sydney property prices. To begin, Belle would like you to run a simple linear regression of price as the dependent variable; and Tincome as the independent variable. As part of your reporting, you need to interpret the coefficients of the model and discuss whether they are economically and statistically significant. Also report the confidence interval of dependent variable (price) and interpret the results. Next, Belle wants you to run a multiple linear regression. As part of this exercise you need to: Explain why a multiple linear regression is beneficial i.e. justify the need for multiple linear regression and the issues associated with running a simple linear regression. Contextualise it in the context of the current problems are there confounding factors which motivate you to do this? Associated with this think about the what type of model you'd like to use e.g. level- level, log-level, log-log or level-log model for each of the considered variables. You need to justify this. Run the model with the following independent variables: No of bedrooms; O Total Income; O Location; Pcondition; o Shops; and Bus. O O and price as the dependent variable. You should also construct at least one interaction variables but it must make sense and must be justified. Creativity will be rewarded if you do this and you (i) construct it correctly, (ii) justify it and (iii) provide an interpretation of this variable. As part of the reporting requirements for the multiple linear regression: . Interpret the coefficients. Define and comment whether each of the coefficients are statistically significant. Remember to state your assumptions. Define and comment whether each of the coefficients are economically significant. Remember to state your assumptions. You'll also need to define what is economically significant and use a benchmark to determine this. Limitations and issues with your model. If you decide to use technical terms e.g. multicollinearity, homoskedasticity, bias, consistency etc. you need to explain what these terminologies are and place them in the context of your problem and how it will affect your results. . C. C. C. a. 1. Chi Squared test - Hypothesis testing (8/100) There are four parts to this: a. Correctly define the null and alternate hypothesis b. Decision rule or P-value approach Test statistic calculation d. Draw the appropriate calculation in the context of the claim. 2. Chi Squared Test - Assumptions (5/100) a. Invoke CLT for large n. b. Define "alpha" or use P-value and discuss the conventional value of "alpha" Others 3. Chi Squared Test - Limitations (5/100) a. Sample subject to errors. b. Outliers that may skew your results (remember you are using the mean). Other 4. Simple linear regression - Running the model and interpretation (12/100) There are five parts to this: Run the model i.e. they report the results b. Marginal effect interpretation c. Statistical significance (one mark deduction if they don't say statistically different from zero or something to that effect.) d. Economic significance (2 marks, one mark deduction if they do not define economic significance properly e.g. do they use a certain benchmark like the average) Limitations of a simple linear regression (confounding factors not accounted for leading to a wrongful interpretation of the coefficients, omitted variable bias is another examples) 5. Simple Linear Regression - Confidence Intervals (8/100) a. Report the confidence interval of price b. Interpretation of the confidence interval of price 6. Multiple linear regression - running the model and interpretation (60/100) There are three parts to this: a. Justification of why a multiple linear regression model is important in this case b. Justification of the functional form C. Creativity use of interaction variables d. Run the model i.e. they report the results e. Marginal effect interpretation e.g. a one unit increase in x suggests a b increase in y (Deduct 0.5 mark for each incorrect interpretation) f. Statistical significance of each of the variables (Deduct for each incorrect statement and if you don't say statistically different from zero or something to that effect.) g Discussion of economic significance (Deduction if they do not define economic significance properly e.g. do they use a certain benchmark like the average) h. Limitations of the model (2 mark for multicollinearity, 2 mark for omitted variable bias, 2 marks for any other. Max of one mark for each if you simply mention the problem e.g. multicollinearity with no explanation). e. SUMMARY OUTPUT Regression Statistics Multiple R 0.05860241 R Square 0.00343424 Adjusted RS -2.191E-06 Standard Err 660937.324 Observations 292 ANOVA df Regression Residual Total SS MS F Significance F 1 4.3656E+11 4.3656E+11 0.99936248 0.31829822 290 1.2668E+14 4.3684E+11 291 1.2712E+14 Coefficients tandard Erroi t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 917880.048 63923.8614 14.3589581 1.0941E-35 792066.517 1043693.58 792066.517 1043693.58 566000 0.26328107 0.26336503 0.99968119 0.31829822 -0.2550682 0.78163031 -0.2550682 0.78163031 Milestone 3 - Model development of property prices Belle also recently heard in the media that the proportion of sales are as follows: . . . 35% of sales are apartments; 45% of sales are houses; 10% of sales are townhouses; 5% of sales are villas and; 5% of sales are other. Belle would like to know if the sample data is statistically different to what the media is suggesting. Remember to state your assumptions and limitations of the result. In addition to this, Belle would like you to develop a propriety model to predict Sydney property prices. To begin, Belle would like you to run a simple linear regression of price as the dependent variable; and Tincome as the independent variable. As part of your reporting, you need to interpret the coefficients of the model and discuss whether they are economically and statistically significant. Also report the confidence interval of dependent variable (price) and interpret the results. Next, Belle wants you to run a multiple linear regression. As part of this exercise you need to: Explain why a multiple linear regression is beneficial i.e. justify the need for multiple linear regression and the issues associated with running a simple linear regression. Contextualise it in the context of the current problems are there confounding factors which motivate you to do this? Associated with this think about the what type of model you'd like to use e.g. level- level, log-level, log-log or level-log model for each of the considered variables. You need to justify this. Run the model with the following independent variables: No of bedrooms; O Total Income; O Location; Pcondition; o Shops; and Bus. O O and price as the dependent variable. You should also construct at least one interaction variables but it must make sense and must be justified. Creativity will be rewarded if you do this and you (i) construct it correctly, (ii) justify it and (iii) provide an interpretation of this variable. As part of the reporting requirements for the multiple linear regression: . Interpret the coefficients. Define and comment whether each of the coefficients are statistically significant. Remember to state your assumptions. Define and comment whether each of the coefficients are economically significant. Remember to state your assumptions. You'll also need to define what is economically significant and use a benchmark to determine this. Limitations and issues with your model. If you decide to use technical terms e.g. multicollinearity, homoskedasticity, bias, consistency etc. you need to explain what these terminologies are and place them in the context of your problem and how it will affect your results. . C. C. C. a. 1. Chi Squared test - Hypothesis testing (8/100) There are four parts to this: a. Correctly define the null and alternate hypothesis b. Decision rule or P-value approach Test statistic calculation d. Draw the appropriate calculation in the context of the claim. 2. Chi Squared Test - Assumptions (5/100) a. Invoke CLT for large n. b. Define "alpha" or use P-value and discuss the conventional value of "alpha" Others 3. Chi Squared Test - Limitations (5/100) a. Sample subject to errors. b. Outliers that may skew your results (remember you are using the mean). Other 4. Simple linear regression - Running the model and interpretation (12/100) There are five parts to this: Run the model i.e. they report the results b. Marginal effect interpretation c. Statistical significance (one mark deduction if they don't say statistically different from zero or something to that effect.) d. Economic significance (2 marks, one mark deduction if they do not define economic significance properly e.g. do they use a certain benchmark like the average) Limitations of a simple linear regression (confounding factors not accounted for leading to a wrongful interpretation of the coefficients, omitted variable bias is another examples) 5. Simple Linear Regression - Confidence Intervals (8/100) a. Report the confidence interval of price b. Interpretation of the confidence interval of price 6. Multiple linear regression - running the model and interpretation (60/100) There are three parts to this: a. Justification of why a multiple linear regression model is important in this case b. Justification of the functional form C. Creativity use of interaction variables d. Run the model i.e. they report the results e. Marginal effect interpretation e.g. a one unit increase in x suggests a b increase in y (Deduct 0.5 mark for each incorrect interpretation) f. Statistical significance of each of the variables (Deduct for each incorrect statement and if you don't say statistically different from zero or something to that effect.) g Discussion of economic significance (Deduction if they do not define economic significance properly e.g. do they use a certain benchmark like the average) h. Limitations of the model (2 mark for multicollinearity, 2 mark for omitted variable bias, 2 marks for any other. Max of one mark for each if you simply mention the problem e.g. multicollinearity with no explanation). e