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# Basic Econometrics Tools

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Basic Econometrics Tools
Correlation and Regression Analysis
Christopher Grigoriou

Executive MBA – HEC Lausanne
2007/2008
1

A collector of antique grandfather clocks wants to know if the price received for the clocks increases linearly with the age of the clocks.
The following model: yi=a0 + a1*x1i + εi , where yi=Auction price of the clock i, x1i=Age of clock (years),
A sample of 32 auction prices of grandfather clocks, along with their age, is given in the next table.
Table 1- Auction price and Age i 1
2
3
4
5
6
7
8
9
10
11
12

Auction
Price, y
1235
1080
845
1522
1047
1979
1822
1253
1297
946
1713
1024

Age, x1 127
115
127
150
156
182
156
132
137
113
137
117

i
13
14
15
16
17
18
19
20
21
22
23
24

Auction
Price, y
1147
1092
1152
1336
2131
1550
1884
2041
845
1483
1055
1545

Age, x1 137
153
117
126
170
182
162
184
143
159
108
175

i
25
26
27
28
29
30
31
32

Auction
Price, y
729
1792
1175
1593
785
744
1356
1262

Age, x1 108
179
111
187
111
115
194
168

2

Correlation analysis (see Appendix 1)

Figure 1- Scatter Plot- Auction Price and Age
2590

Auction Price, y

2 09 0

1 590

1 09 0

590

90
1 00

125

150

175

2 00

Age, x1

From this figure => positive correlation between Auction price and Age?

3

=> Correlation coefficient

Outil/Utilitaire d'Analyse/ Analyse de correlation/plages d’entrée/de sortie/ok
-1 ≤ rx,y ≤ +1 rx,y ≤ 0 => negative correlation ; rx,y ≥ 0 => positive correlation rx,y = 0 => no linear correlation rx,y = ± 1 => perfect correlation
The relationship we consider is LINEAR!
Correlation does not mean causality

Spurious correlation (e.g.: population in Egypte and Economic growth in China)

Reversal causality
4

One step further : the simple regression...

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