252blunders 12/3/07
Regression Blunders
The Lees say that the percent that vote for the incumbent (percent) is determined in part by the growth rate
of disposable income (%DI). Do a regression to test this theory.
Row
1
2
3
4
5
6
7
8
9
10
percent %DI
45.0 1.2
48.0 1.8
49.5 2.0
48.8 1.9
50.4 2.2
51.3 2.4
52.4 2.7
47.6 1.9
54.1 3.0
50.0 2.3
497.1 21.4
%DIsq
1.44
3.24
4.00
3.61
4.84
5.76
7.29
3.61
9.00
5.29
48.08
percentsq
2025.00
2304.00
2450.25
2381.44
2540.16
2631.69
2745.76
2265.76
2926.81
2500.00
24770.9
First, if you have to ask which is x and which is y, you should not be taking the final exam!
y  497 .1 ,
x  21 .4 ,
y 2  24770 .9 and
x 2  48 .08
That said, we have here




 xy .
  y  y x  x  and you believe that you can compute these
Second, if you are using the formula b 
 x  x 
y  49.71 , x  2.14 . I have not computed
2
sums without first computing four more columns, you are wasting your time. If you compute the four
columns, when you have the formula b1 
S xy
SS x

 XY  nXY
 X  nX
2
2
instead, you are still wasting your time.
48 .08
, you had better try studying.
10
Fourth, if you think n  20 , wake up!
Third, if you think that x 2 
Fifth, if you think that
y
2
 xy  497 .121.4 or  xy  497 .1  21.4 or  y
2
 497.12 or
 497.12 you are dreaming. Of course, maybe there is an Easter bunny.
Sixth, if you think SSx , SSy or R 2 can be negative, think again! (Of course, S xy can have any sign it
wants.)
Seventh, if you think R 2 can be above 1, you have no idea what R 2 is!
Eighth, if you think that a p-value or any other probability can be above 1 or below zero, you should repeat
ECO251.
The solution to all these problems is, of course, study!
Incidentally, if you want to propose a good alternative to the other problems proposed for Computer
Problem 4, try the problem above looking at the last 10 elections. I would strongly advise finding
another data source, since I have no idea what years are used above. The other independent variables
are the inflation rate and the unemployment rate. Or you could try replacing these two with the
misery index, which is just the sum of inflation and unemployment. You could also try a dummy
variable for wartime.