Question

Section C (20 Marks) C1 :Below you are given a partial ISD1: 10 marks] computer output based on a sample of 40 observations. Coefficient Standard Error Constant 25.848 8.85 7.364 K 90.432 5.26 X2 25.12 Analysis of Varianee Sum of Mean Source of Degrees s Square Variation Regression Error of Freedom Squares 4,853 970.6 1. Use the output shown above and write the estimated regression equation. (2 marks) Interpret the meaning of the coefficient of X1 and X2. (2 marks) 3. Compute the test statistic required to kno marks) 4. What is the t value obtained from the table which is used to test an individual parameter at the 1% level? (2 marks) 5. Compute the degrees of freedom for the sum of squares explained by the regression (SSR). (2 marks) Required: w whether the parameter βι is significant. (2

Answer 1

1.

Dependent variable (Y) = 25.848 - 7.364 * X1 + 90.432 * X2

2.

The coefficients are the respective slope parameters for X1 and X2 respectively. In other words, they are the rate of change of the dependent variable value per unit change of independent variables' value.

3.

β1 is the coefficient of X1.

Test statistic, t = -7.364 / 5.26 = -1.40

4.

The t distribution value for 99% significance is computed using Excel function =T.INV.2T(0.10, df)

No obs. = 40, so, total degrees of freedom = 39
Degrees of freedom for regression = 2 (since there are three parameters, β0, β1, and β2, so, df = 3 -1 = 2)
So, degrees of freedom for the residual = 39 - 2 = 37

So, the t distribution value for 99% significance =T.INV.2T(0.10, 37) = 1.687

5.

SS explained by regression = 2 (since there are three parameters, β0, β1, and β2, so, df = 3 -1 = 2)