Question

Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The following values are relevant for assessing goodness of fit of the estimated model with the exception of

• A. 0.130357
• B. 8.769363
• C. 1.46693
• D. none of these

Answer 1

In order to find the goodness of fit, we will try to test whether the regressor in the model is statistically significant.

If it does appear to be significant, then we can say that the model has a good fit and so on.

As there is only a single regressor, it tantamounts to checking out whether the slope coefficient is significantly different from 0.

Hence, we test :

The appropriate test statistic is a t variable which is given as :

b1 / se(b1)

Now, let's look at the options.

The first option is the value of R square which gives us an idea whether the model has enough explanatory power. This has a bearing on the goodness of fit.

The second option is the value of SER. In general, lower the SER, better is the fit of the model.

The third option is used to calculate the test statistic to test goodness of fit.

Hence, the correct answer will be none of the above as both option 1, 2 and 3 are relevant in the calculation of goodness of fit.