Question

1) Using the table below, complete the questions that follow (econometrics)

Source I MS 20 Number f obs F( 2, 17)= C Prob > E R-squared Adj R-squared 0.8036 df Model A B 2.2209e+15 0.0000 Residual 9.4671e+14 17 5.5689e+13 Total 5.3885e+15 E 2.8361e+14 Root MSE 7 . 5e+06 = BOXOfficeRev-e Coef. Std. Err t P>t [95% Conf. Interval] StarPowerIndex I 443695 294622.8 1.51 0.150 -177904.8 F Actionindex 561704.2G 7.30 0.000 399338 724070.4 cons I 7083228 -1.25 0.227-2.38e+07 6073458

a) Using the table above, which coefficients are statistically significant? And is the model significant?

b) Give me the equations to calculate the following a t-stat, an f-stat, coefficient in an SLR, and a Standard Error.

c) What are the 6 Gauss-Markov Assumptions and what, when met, do they say about our linear model.

d) What is the t-stat for a 95% confidence interval, with 522 degrees of freedom? What does the critical value mean? Would we reject the null hypothesis with a t-stat of 2.45?  

Answer 1

Ans a) The coefficient of variable Actionindex with a p-value of 0.0000 is stattistically significant. All other variables have a high p-value and thus lie in the rejection zone giving us sufficient evidence to reject their significance.

The model is significant as Prob > F = 0.0000 which gives sufficient evidence to accept the significance of the model.

Ans b)

$t=(\hat{\beta -\beta })/(se(\hat{\beta }))$

$F=((SSR/k)/(SSE/(n-k-1)))$

Here, SSR = A, k = B, SSE = 9.4671e+14, (n-k-1) = 17

$\hat{\beta } = (\sum xy - n\bar{x}\bar{y})/(\sum x^{2} - n\bar{x}^{2})$ is the slope coefficient

$\hat{\alpha } = \bar{y} - \hat{\beta } \bar{x}$

$se (\hat{\beta }) = \sqrt{SSE/(n-2)}$ is the standard error of slope coefficient

Ans c) The Gauss Markov Assumptions are -

(i) The regression model is linear in parameters

(ii) Expected value of the error term is zero

(iii) Error terms are uncorrelated. This is the assumption of no autocorrelation.

(iv) Error terms have a constant variance. This is the assumption of homoskedasticity.

(v) The error terms and the explanatory variables are uncorrelated. This means there is no endogeneity.

(vi) The explanatory variables are uncorrelated. This means there is no perfect multicollinearity.

When met, we can say that the parameters of the linear model are Best Linear Unbiased Estimators (BLUE).

Ans d) With 522 degrees of freedom, and at 95% C.I. the t-stat value is +/- (1.9645).

Critical value is the value on the scale of the test statistic after which we can no longer accept the null hypothesis. The level of significance of the test signifies this value.

The null hypothesis with a t-stat of 2.45 will be rejected because it will lie in the rejection region that is between the confidence interval mentioned above.