Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
GOODNESS OF FIT
Four useful results:
e 0
Y Y
X e
i i
0
Y e
i i
0
This sequence explains measures of goodness of fit in regression analysis. It is
convenient to start by demonstrating three useful results. The first is that the mean value
of the residuals
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
EXERCISE R.13
R.13 Let HT be the correlation between humidity, H, and
temperature measured in degrees Fahrenheit, F.
Demonstrate that the correlation coefficient is unaffected
if temperature is instead measured in degrees Celsius, C.
Note: C = 5/9(F 32).
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
EXERCISE 5.5
The Stata output shows the result of a semilogarithmic regression of
earnings on highest educational qualification obtained, work
experience, and the sex of the respondent, the educational
qualifications being a professional degree, a PhD, a
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
EXERCISE 1.5
1.5
The output below shows the result of regressing the weight
of the respondent in 1985, measured in pounds, on his or
her height, measured in inches. Provide an interpretation
of the coefficients.
. reg WEIGHT85 HEIGHT
Source 
SS
df
MS
+
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
EXERCISE 1.16
1.16
The output below shows the result of regressing weight in
2002 on height, using EAEF Data Set 21. In 2002 the
respondents were aged 3744. Explain why R2 is lower
than in the regression reported in Exercise 1.5.
. reg WEIGHT02 HEIGHT
Sou
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
1.1
ECONOMETRICS
by
N V M Rao
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE,
PILANI
RAJASTHAN
2013
NVM
1.2
Course No. : ECON C342/FIN C332/ MGTS C443
Course Title : ECONOMETRICS
&
Course No. : ECON F241
Course Title : ECONOMETRIC METHODS
Instructorincharg
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
F TEST OF GOODNESS OF FIT
Var(Y ) Var(Y ) Var(e )
(Y Y ) 2 (Y Y )2 e 2
TSS ESS RSS
In an earlier sequence it was demonstrated that the variance of the actual values of Y could
be decomposed into the variance of the fitted values and the variance of the re
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
AUTOCORRELATION IN A MODEL WITH A LAGGED DEPENDENT VARIABLE
Yt 1 2 X t 3Yt 1 u t
It has been mentioned in a previous sequence that, in a regression model where a lagged
dependent variable is one of the explanatory variables, OLS estimates will be subject
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
GOODNESS OF FIT
Three useful results:
e 0
Y Y
Cov(Y , e ) 0
This sequence explains measures of goodness of fit in regression analysis. It is
convenient to start by demonstrating three useful results. The first is that the mean value
nvmrao
of the residual
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
1A.1
Review
Some Basic
Statistical Concepts
1A.2
Many of the things we will be interested in this class are
random variables (RVs); that is, variables whose outcome
is subject to chance.
We do not know what value a RV will take until we observe
it.
Exampl
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
Graphical Methods
Plot residuals Across Time
Plot residuals and Lagged Values in 4Quadrant Diagram
Von Neumann Ratio Test
DW Test
DurbinWatson Test
The DurbinWatson test is by far the most
important one for detecting AR(1) errors.
It is assumed t
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
METHODOLOGY OF ECONOMETRICS
Broadly speaking, traditional econometric methodology proceeds
along the following lines:
1. Statement of theory or hypothesis.
2. Specification of the mathematical model of the theory
3. Specification of the statistical, or e
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
CONFIDENCE INTERVALS
probability density function of b2
null hypothesis
0
H0: 2 = 2
0
conditional on 2 = 2 being true
2.5%
0
21.96sd
2.5%
0
2sd
0
2
0
0
2+sd 2+1.96sd
In the sequence on hypothesis testing, we started with a given hypothesis, for exampl
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
FOOTNOTE: THE COCHRANEORCUTT ITERATIVE PROCESS
yt xt ut
ut ut 1 t
yt 1 xt 1 ut 1
yt yt 1 (1 ) xt x t 1 ut ut 1
yt (1 ) yt 1 x t xt 1 t
We saw in the previous sequence that AR(1) autocorrelation could be eliminated by a
simple manipulation of the model. T
Birla Institute of Technology & Science, Pilani  Hyderabad
ECON 221

Fall 2014
TYPE I ERROR AND TYPE II ERROR
hypothetical distribution
0
under H0 : 2 2
acceptance region for b2
5% level
2.5%
2.5%
0
0
21.96sd 2sd
0
2
0
0
2+sd 2+1.96sd
b2
In the previous sequence a Type I error was defined to be the rejection of a null hypothesis