Question

Question: Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05).

The estimated regression equation for a model involving two independent variables and 65 observations is:

yhat = 55.17+1.1X₁ -0.153X₂

Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, S_b1 = 0.33, S_b2 = 0.20.

Answer 1

The model being estimated is

$Y=\beta_0+\beta_1X_1+\beta_2X_2+\epsilon$

where $\beta_0$ is the intercept

$\beta_1,\beta_2$ are the slope coefficients for

1

is a random disturbance

2ad ENN(0, 0

to test whether the overall model is significant, the hypotheses are

Ho 120null hypothesis: The independent variables cannot explain Y H4 at least one of 61, 620 alternative hypothesis: The overall model is significant 0.05level of significance to test the hypotheses

n=65 is the number of observations

k=2 is the number of independent variables

The sum of square regression (SSR) is

SSR 12370.8

The degrees of freedom for SSR = k=2

The sum of square total is

SST35963.0

The sum of square errors is

SSE SST-SSR 35963.0 12370.8 23592.2

The degrees of freedom for SSE = n-k-1=65-2-1=62

The F statistics is

12370.8/2 SSR/k 16.26 F sSE/(n k 1 23592.2/(65 2 1)

ans: F statistics is 16.26

The numerator degrees of freedom =2 and the denominator df=62

The using the F table for alpha=0.05 and numerator degrees of freedom =2 and the denominator df=60 (the closest to 62), we get a critical value of 3.15.

We will reject the null hypothesis if the test statistics is greater than the critical value for alpha=0.05.

Here, the test statistics is 16.26 and it is greater than the critical value 3.15. Hence we reject the null hypothesis.

ans: We conclude that there is sufficient evidence to support the claim that  the overall model is significant.