1. Diploma in Statistics Introduction to Regression Lecture 4.11 Introduction to Regression Lecture 4.1 1.Review Lecture 3.1 2.Review Laboratory Exercise 3.Introducing indicator variables –Housing completions case study

2. Diploma in Statistics Introduction to Regression Lecture 4.12 Regression 1971-1983 \ 1979 Predictor Coef SE Coef T P Constant 327.99 29.03 11.30 0.000 GNP -0.05480 0.01664 -3.29 0.011 RLP -56.65 13.45 -4.21 0.003 RPC 29.50 46.78 0.63 0.546 S = 5.8924

3. Diploma in Statistics Introduction to Regression Lecture 4.13

4. Diploma in Statistics Introduction to Regression Lecture 4.14

5. Diploma in Statistics Introduction to Regression Lecture 4.15 Regression 1971-1983 1979, 1980, RPC excluded Predictor Coef SE Coef T P Constant 339.58 10.62 31.96 0.000 GNP -0.03158 0.01329 -2.38 0.045 RLP -70.155 9.660 -7.26 0.000 S = 3.92988 R-Sq = 96.8%

6. Diploma in Statistics Introduction to Regression Lecture 4.16 Exercise Calculate the predicted stamp sales for 1984 and 1985. Assume no change in nominal stamp price. Compare with the actual outcomes: 19841985 Sales163.6172.1 GNP1487.51466.6 RLP1.8351.741 Comment on the prediction errors.

7. Diploma in Statistics Introduction to Regression Lecture 4.17 Exercise Predicted Sales = 340 –.0316 GNP – 70.12 RLP To calculate the predicted sales for any year, find the values of GNP and RLP for that year and substitute them in the equation. Problem:how to get GNP and RLP for future years? Answer:use "official" predictions.

8. Diploma in Statistics Introduction to Regression Lecture 4.18 Central Bank predictions for 1984, 1985 19841985 GNP:+ 1.5%+ 1.5% Inflation:+ 8.6%+ 5.5% NB:no change in nominal stamp price in 1984 or 1985 GNP(83) = 1462.6; predicted GNP(84)= 1462.6 × 1.015 = 1484.5 RLP(83) = 1.993; assuming no change in nominal stamp price, predicted RLP(84)= 1.993 / 1.086 = 1.835

9. Diploma in Statistics Introduction to Regression Lecture 4.19 Central Bank predictions for 1984, 1985 RLP(83) = 1.993; assuming no change in nominal stamp price, predicted RLP(84)= 1.993 / 1.086 = 1.835 The REAL letter price for 1984 is lower than RLP(83), RLP(84) has to be increased by 8.6% to bring it to 1983 levels, RLP(84) × 1.086 = RLP(83) i.e., RLP(84) = RLP(83) / 1.086

10. Diploma in Statistics Introduction to Regression Lecture 4.110 Prediction for 1984 GNP(84) = 1484.5 RLP(84) = 1.835 Predicted Sales = 340 –.0316 × GNP – 70.12 × RLP = 340 –.0316 × 1484.5 – 70.12 × 1.835 = 164.4 Actual outcome: 163.6 Prediction for 1985?Homework 3.1.1

11. Diploma in Statistics Introduction to Regression Lecture 4.111 Homework 3.1.2 Carry out the analysis of stamp sales data prior to 1970, leading to the prediction formula Sales = 371 – 176 RLP + 84 RPC, s = 5.5. Compare early and recent prediction formulas, including prediction errors. Ref:SA pp. 282-4

12. Diploma in Statistics Introduction to Regression Lecture 4.112 Homework 3.1.2

13. Diploma in Statistics Introduction to Regression Lecture 4.113 Introduction to Regression Lecture 4.1 1.Review Lecture 3.1 2.Review Laboratory Exercise 3.Introducing indicator variables –Housing completions case study

14. Diploma in Statistics Introduction to Regression Lecture 4.114 Introduction to Regression Lecture 4.1 1.Review Lecture 3.1 2.Review Laboratory Exercise 3.Introducing indicator variables –Housing completions case study

15. Diploma in Statistics Introduction to Regression Lecture 4.115 A strategic forecasting problem Grafton Group plc. is an independent, profit growth oriented company operating in Great Britain and Ireland whose main activities are builders and plumbers merchanting, DIY retailing and strategic manufacturing in related areas. The group aims to achieve above average returns for its shareholders. Grafton strategy is to maintain strong positions in business serving the British and Irish building sectors, to develop in other British and Irish markets, and to grow in businesses with which it is familiar.

16. Diploma in Statistics Introduction to Regression Lecture 4.116 A key factor affecting the Group's trading level is the number of new houses being built. This has strategic implications for the development of the company. Knowledge of this will assist in determining future levels of investment and consequent staffing levels. It will also provide assistance in making profit projections required by the Stock Exchange. In 2001, the company embarked on a project to better understand the new housing market in Ireland. As a first step towards strategic decision making, a company executive had acquired data on numbers of housing completions in Ireland, quarterly from 1978 to 2000. The data are shown in Table 1.6

17. Diploma in Statistics Introduction to Regression Lecture 4.117 Table 1.6Housing Completions, quarterly, 1978 to 2000

18. Diploma in Statistics Introduction to Regression Lecture 4.118 Figure 1.30Housing Completions, quarterly, 1978 to 2000 Q1 1981 Q1 1993 Q1 1989

19. Diploma in Statistics Introduction to Regression Lecture 4.119 Figure 1.31Housing Completions, quarterly, 1993 to 2000

20. Diploma in Statistics Introduction to Regression Lecture 4.120 Figure 1.32Housing Completions, quarterly, 1993 to 2000, with quarterly trends

21. Diploma in Statistics Introduction to Regression Lecture 4.121 Model formulation Completions =  +   Time + . Predicted completions = 3937 + 259  Time.

22. Diploma in Statistics Introduction to Regression Lecture 4.122 Table 1.7Completions and Quarterly Indicators

23. Diploma in Statistics Introduction to Regression Lecture 4.123 Model formulation Completions =  1  Q 1 +  2  Q 2 +  3  Q 3 +  4  Q4 +   Time + . Quarter 1:Completions =  1 +   Time Quarter 2:Completions =  2 +   Time, Homework 4.1.1:Write down the prediction formulas for future third and fourth quarters.

24. Diploma in Statistics Introduction to Regression Lecture 4.124 Reading SA §1.7, §8.7