Question

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable (x) and a dependent variable (y). Coefficient Standard Error 7.032 0.184 t-Stat -1.3456 4.1793 Intercept Analysis of Variance SOURCE Regression Error (Residual) 400 138 a. Develop the estimated regression line. b. At a = 0.05, perform an F test. C. Determine the coefficient of determination.

Answer 1

a)

Using t-statistic formula:

Ustaistic coefficient SE(coefficient)

let us first estimate both coefficients:

tutaisticos – 4.1793 – ondas

b1 = 4.1793 * 0.184 = 0.76899 0.769

Similarly,

bo tstaisticho — She bo -1.3456 = 5 7.032

bo= -1.3456 * 7.032 = 9.462259 -9.4623

Hence equation of estimated regression line is:

y = -9.4623 +0.769.c

b)

Let us test significance of linear relationship between x and y.

Thus our null hypothesis:

HO: B1 = 0

Vs alternative hypothesis:

H1:31 0

Level of significance,

g= 0,05

Degrees of freedom for regression = number of predictor variables = 1

DF numerator = 1

Degrees of freedom for residual = n - 2 = 8 - 2 = 6

DF denominator = 6

Therefore,

Fcritical = F(DE,,DF, a) = F(1,6,0.05) = 5.9874

Test statistic:

We know that,

$MSR=\frac{SSR}{df}=\frac{400}{1}=400$

MSE – SP 19 23

400 F MSR Var = = = 17.39

Fstat > Fcritical

We reject null hypothesis.

p-value approach:

p-value = PF > 17.39) = 0.0059

Hence,

p - value <a

We reject null hypothesis.

There is sufficient evidence to support the linear relationship between x and y.

c)

SSR. SSR 400 400 R? – SSR SSR SSR + SSE 400128 = 20 = 0.74349