PRACTITIONERS' CORNER: The Coefficient of Determination for a Regression Model Based on Group Data
| Published date | 01 May 1993 |
| DOI | http://doi.org/10.1111/j.1468-0084.1993.mp55002007.x |
| Author | N. Kakwani |
| Date | 01 May 1993 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 55,2 (1993)
0305-9049 S3.00
PRACTITIONERS' CORNER
The Coefficient of Determination for a Regression
Model Based on Group Data
N. Kakwanit
I. INTRODUCTION
The coefficient of determination is defined as the proportion of total varia-
tion in the dependent variable y that is explained by the regression equation.
If we are estimating the regression equation from the grouped data, the total
variation in y cannot be measured. In this paper, we therefore define the
coefficient of determination for grouped data as the proportion of between
group variation in y that is explained by the regression. We demonstrate that
this measure of goodness of fit is superior to the one commonly used
(Kmenta, 1990). It is identical to the usual R2 for individual observations if
each group has only one observation and also, it is directly related to a simul-
taneous testing of hypothesis on regression coefficients. A numerical illustra-
tion presented in the paper is based on the National Sample Survey data on
consumer expenditure for the year 1983, covering the entire rural area of
India.
II. NOTATION
Let us consider a multiple regression model
y = Xß + u (1)
where y is a vector of n individual observations on the dependent variable, X
is the n X k matrix of observations on the k independent variables. The first
colunm of X has all elements equal to one. ß is the coefficient vector and u is
a vector of n disturbances.
We assume that the disturbances in (1) have zero mean and constant
variance, and are independently distributed:
Eu =0, Euu'=u21,
fi would like to thank Dr Eric Sowey for his helpful comments on this note.
245
To continue reading
Request your trial