Introduction to Regression Lecture 4.1

1. Introduction to RegressionLecture 4.1 • Review Lecture 3.1 • Review Laboratory Exercise • Introducing indicator variables • Housing completions case study Diploma in Statistics Introduction to Regression

2. 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 Diploma in Statistics Introduction to Regression

3. Diploma in Statistics Introduction to Regression

4. Diploma in Statistics Introduction to Regression

5. Regression 1971-19831979, 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% Diploma in Statistics Introduction to Regression

6. Exercise Calculate the predicted stamp sales for 1984 and 1985. Assume no change in nominal stamp price. Compare with the actual outcomes: 1984 1985 Sales 163.6 172.1 GNP 1487.5 1466.6 RLP 1.835 1.741 Comment on the prediction errors. Diploma in Statistics Introduction to Regression

7. 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. Diploma in Statistics Introduction to Regression

8. Central Bank predictions for 1984, 1985 1984 1985 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 Diploma in Statistics Introduction to Regression

9. 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 Diploma in Statistics Introduction to Regression

10. 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 Diploma in Statistics Introduction to Regression

11. 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 Diploma in Statistics Introduction to Regression

12. Homework 3.1.2 Diploma in Statistics Introduction to Regression

13. Introduction to RegressionLecture 4.1 • Review Lecture 3.1 • Review Laboratory Exercise • Introducing indicator variables • Housing completions case study Diploma in Statistics Introduction to Regression

14. Introduction to RegressionLecture 4.1 • Review Lecture 3.1 • Review Laboratory Exercise • Introducing indicator variables • Housing completions case study Diploma in Statistics Introduction to Regression

15. 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. Diploma in Statistics Introduction to Regression

16. 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 Diploma in Statistics Introduction to Regression

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

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

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

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

21. Model formulation Completions = a + b Time + e. Predicted completions = 3937 + 259  Time. Diploma in Statistics Introduction to Regression

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

23. Model formulation Completions = a1Q1 + a2Q2 + a3Q3 + a4Q4 + b Time + e. Quarter 1: Completions = a1 + b Time Quarter 2: Completions = a2 + b Time, Homework 4.1.1: Write down the prediction formulas for future third and fourth quarters. Diploma in Statistics Introduction to Regression

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