Question

An analyst is running a regression model using the following data:

Y	x1	x2	x3	x4	x5	x6
4	1	5	0	-95	17	12
10	5	8	1	-27	7	10
32	1	7	0	-82	0	9
2	2	7	0	17	5	10
9	3	9	1	-46	5	11

Excel performs the regression analysis, but the output looks all messed up: For example the F statistic cannot be computed, standard errors are all zero, etc etc.

What is wrong here, and why does it make no sense to run this ordinary least squares regression in the first place? Explain in detail!

Answer 1

For the regression analysis, the number of observations should be greater than the number of parameters in the model. In this question, the number of observation is 5 (n=5, length of the variable y or any explanatory variables) whereas the number of the parameters in the model are 8 ( 1 for the intercept, 6 for the slopes of x1, x2, x3, x4, x5, x6 and 1 for the variance). Due to this result, you can to estimates the parameters, test statistics, standard errors etc.