The learning outcomes of this topic are: - Evaluate results from regression analysis - Interpret results from regression analysis - Recognise the possibility to extend regression analysis (dummy variables)

1. Topic 8:
Regression Analysis 2

2. This topic will cover:
◦ Regression using software
◦ Multiple linear regression
 Extending regression models with dummy
variables
 Interpreting models

3. By the end of this topic students will be able
to:
◦ Evaluate results from regression analysis
◦ Interpret results from regression analysis
◦ Recognise the possibility to extend regression
analysis
 Dummy variables

4. • For the least SSE straight line,
y = mx + c
m =
n xy − x y
n x2 − x 2
c = y − mx
R =
n xy− x y
n x − x 2 n y2 − y 2

5. x y
25 1.44
50 5.58
75
14.6
4
100 6.94
x y
25 3.07
50 5.64
75 9.63
100
10.2
6

6. ◦ Many software packages
 OpenOffice, Gretl
 MS Excel
 SPSS, Minitab, SAS
 R, S
◦ MS Excel
 2007/2010 Data/Data Analysis/Regression
 Older Tools/Data Analysis/ Regression
 Then all versions are similar

9. ◦ Reasons Not to Set Constant Term to Zero
 It prevents model being biased
 Usually interested in the predictor variables anyway
 You don’t need to collect data for it
 Can help if data is only locally linear
◦ Reason to Set constant Term to Zero
 If it is supposed to be zero
 Strong theoretical grounds
 But care needed with calculation and
interpretation of R2

11. ◦ Models such as
y = c + b1x1+ b2x2+ ...
◦ How are they developed?
 an expert task
◦ Managers
 understand
 question
 use results

12. ◦ Estate agent (realtor) is establishing an office in a
new location
◦ Wishes to build a model of advertised prices
◦ Collects competitor data on;
 Internal area
 Land
 Distance from nearest school
 City region

13. Property Price School Land Area District
1 457 3 1791 165 FD
2 487 1 800 177 FD
3 218 3 759 94 FD
4 300 4 829 137 FD
5 358 2 630 110 AC
6 658 1 655 201 AC
7 402 2 999 85 AC
8 541 2 920 146 AC
9 358 3 1185 112 Other
10 444 1 787 155 Other
11 298 3 597 180 Other
12 462 1 1447 200 Other

14. Property Price School Land Area AC FD District
1 457 3 1791 165 0 1 FD
2 487 1 800 177 0 1 FD
3 218 3 759 94 0 1 FD
4 300 4 829 137 0 1 FD
5 358 2 630 110 1 0 AC
6 658 1 655 201 1 0 AC
7 402 2 999 85 1 0 AC
8 541 2 920 146 1 0 AC
9 358 3 1185 112 0 0 Other
10 444 1 787 155 0 0 Other
11 298 3 597 180 0 0 Other
12 462 1 1447 200 0 0 Other

15. price =
constant +
a x (km from a school) +
b x (land in m2) +
g x (floor area in m2) +
d (if in AC) +
z (if in FD)

17. New Worksheet
Response
Predictors

19. R2 =
y − y 2
y − y 2
R
2
= 1- (1 - R2)
n −1
n − k − 1

24. ◦ Equation
 expected price = 45.72 + (2.179 x area) +
(148.8 x AC)
◦ Suppose property is in AC and is of 100m2 what is
expected advertised price?
 expected price = 45.72 + (2.179 x 100) +
(148.8 x 1)
 expected price = 412.42

25. By the end of this topic students will be able
to:
◦ Evaluate results from regression analysis
◦ Interpret results from regression analysis
◦ Recognize possibility to extend regression analysis
 Dummy variables

26. ◦ Hinton, PR. Statistics Explained. Routledge
◦ Keast, S. and Towler M. Rational Decision Making
for Managers. Wiley
◦ Wisniewski, M. Quantitative Methods for Decision
Makers. FT Prentice Hall

27. Any Questions?