Tutorial 3

1. Tutorial 3 Inferential Statistics, Statistical Modelling & Survey Methods (BS2506) Pairach Piboonrungroj(Champ)me@pairach.com

2. 1. House price (Again) Analysis of Variance (ANOVA)

3. 1 (a) (i) Write out the estimated regression equation

4. 1 (a) (ii) Test for the significance of regression equation At 1% Step1: Critical Value Step2: t-Statistic

5. 1 (a) (ii) Test for the significance of regression equation Step1: Critical Value At 1% Step2: t-Statistic > 3.1058 Reject H0 Do NOT Reject H0 < 3.1058 < -3.1058 Reject H0

6. 1. a). (iii) What are DF for SSR & SSE? Analysis of Variance (ANOVA)

7. 1. a). (iv) Test for Significant relationship X&Y? H0: H1: At least one of the coefficients does not equal 0 Analysis of Variance (ANOVA) At Critical Value Then we can reject Null hypothesis, there is a relationship between Xs & Y

8. 1. a). (v) Compute the coefficient of determination and explain its meaning R2 Analysis of Variance (ANOVA) R2 = 1 – (34,727/312,622) R2= 1 – 0.111 R2= 0.889 = 88.9%

9. 1(b) Model 1 Model 2 Model 3

10. 1(b) (i) Compute Adjusted Coefficient of determination for three models

11. 1(b) (ii) Interpret the coefficients on the house type, Beta5 and Beta6 (model 2) Prices for Detached houses increase by £63,794 Prices for Terrace Houses decreased by £65,371 (relative to Semi- detached)

12. 1(b) (iii) At 0.05 level of significance, determine whether model 2 is superior to model1 Model 1 Model 2 Significant i.e., Model 2 is better than Model 1

13. 1(b) (iv) At 0.05 level of significance, determine whether model 3 is superior to model 2 Model 2 Model 3 NOT Significant i.e., Model 3 is NOT better than Model 2

14. 1(b) (v) From model2, estimate the price of 5 years old detached house with 250 square meters

15. 2. Advertising expenditure Analysis of variance Variables in the Equation

16. 2.(a) State the regression equation for the curvilinear model. Variables in the Equation

17. 2.(b) Predict the monthly sales (in pounds) for a month with total advertising expenditure of £6,000

18. 2.(c) Determine there is significant relationship between the sales and advertising expenditure at the 0.01 level of significance H0: H1: At least one of the coefficients does not equal 0 Analysis of variance At Critical Value Then we can reject Null hypothesis, there is a curvilinear relationship between sales and advertising expenditure

19. 2 (d) Fit a linear model to the data and calculate SSE for this model

20. 2 (d) Fit a linear model to the data and calculate SSE for this model

21. 2 (d) Fit a linear model to the data and calculate SSE for this model

22. 2 (d) Fit a linear model to the data and calculate SSE for this model

23. 2 (d) Fit a linear model to the data and calculate SSE for this model

24. 2 (d) Fit a linear model to the data and calculate SSE for this model

25. 2 (d) Fit a linear model to the data and calculate SSE for this model

26. 2 (d) Fit a linear model to the data and calculate SSE for this model

27. 2(e) At 0.01 level of significance, determine whether the curvilinear model is superior to the linear regression model Curvilinear Model Linear Regression Model Significant i.e., Curvilinear effect make significant contribution and should be included in the model.

28. 2 (f) Draw a scatter diagram between the sales& Advertising expenditure.

29. 2 (f) Sketch the Linear regression Linear Regression

30. 2 (f) Sketch the Quadratic regression Quadratic Regression Linear Regression

31. Thank youDownload this Slides atwww.pairach.com/teaching Q & A