Question

Question 3 3 pts Suppose that you estimate a regression model with a sample size of 112 observations and 10 explanatory variables, including the intercept, using ordinary least squares and the residual sum of squares from this estimated model is 22. You then conduct a Ramsey's RESET on this model and the residual sum of squares from the Ramsey regression is 20. The test statistic associated with this Ramsey's RESET is and you can conclude at the 5- percent level of significance that 2; the regression is not misspecified. O 5; the regression is misspecified. 1; the regression is not misspecified. O 4: the regression is misspecified. 3 pts

Answer 1

Ans)- Given

No. of observation (n)=112

Explanatory variable = 10 (including intercept)

Residual sum of squared of main model i.e. restricted model, (RSS_R)= 22

Ramsey’s RESET auxiliary regression is a regression of dependent variable on every explanatory variable, square of dependent variable and cube of dependent variable.

This auxiliary regression is said unrestricted model.

Residual sum of square of this model (RSS_UR) = 20

Setting hypothesis:

H₀ : The restriction impose is true i.e. no specification error in the model

H₁ : There is a specification error in the model

Using F-Statistic

RSSR - RSSUR m F RSSUR) Fam,n-k n-k

Where, RSS_R =22, RSS_UR = 20, n=102

m: is the no. of extra explanatory variable in auxiliary regression in comparison to main model

here square of dependent variable and cube of dependent variable is extra in auxiliary regression.

So, m=2

And k: total no. of explanatory variable in auxiliary or unrestricted model i.e. k = (10+2) =12

Put the values in test statistic

F= 22 - 20 2 20 112 – 12 5

So, in this question the value of Ramsey’s RESET test static is 5.

Now, Tabular of value of test static, F value from table with degree of freedom of numerator (m=2), degree of freedom of denominator (n-k=100) and significance level (α=5% =0.05) i.e. F_0.05,2,100 = 3.07.

Since, the calculated value of F static is less than calculated (3.07 < 5), so we reject the null hypothesis. Hence the model has specification error or the regression is mis-specified.

Hence, here option (b) is correct. i.e. 5; the regression is mis-specified.