Question

2. The estimated regression equation for a model involving two independent

variables and 65 observations is: yhat = 55.17+1.2X1 -0.163X2

Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, Sb1 = 0.33, Sb2 = 0.20. (16 points)

1. Interpret b1 and b2 in this estimated regression equation
2. Predict y when X1 = 65 and X2 = 70.
3. Compute R-square and Adjusted R-Square.
4. Comment on the goodness of fit of the model.
5. Compute MSR and MSE.
6.    Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05).

7. Perform a t test using the critical value approach for the significance of β1.

Use a level of significance of 0.05.

8. Perform a t test using the critical value approach for the significance of β2.

Use a level of significance of 0.05.

3

Answer 1

The estimated regression equation is

a. The coefficient b1=1.2 which is the increase in the y for a unit change in X1. ie when x1 is increased by 1 unit, the value of the dependent variable increases by 1,2 units. the estimate of b2 is -0.163. This indicates that when X2 is increased by 1 unit, the value of Y decreases by -0.163 units.

b. When X1 = 65 and X2 = 70, the estimate of y is

c. The is given by

Adjusted is given by

  

  

  

d. The adjusted is 0.3228 or the model could account for 32.28% of the variation in the data. This means that the model may not be a right fit.

e. The SSE is given by SSE= SST-SSR=35963-12370.8=23592.2

The df for Total=65-1=64

Regression=3-1=2

Error df=64-2=62

The MSR=SSR/2=6185.4, MSE=23592.2/62=380.5194

f. The F statistic is given by . The critical value of F(2,62)=3.1453. Since, the calculated F>the critical value, the regression is significant.

g.

t statistic for b1, . The critical value at 62 df is 1.9989. Since the calculated value of t >the critical value and we reject the null hypothesis and conclude that the parameter b1 is significant and cannot be dropped.

h. For b2, the test statistic is

Since the calculated value of t<the critical value, we fail to reject the null hypothesis and conclude that the parameter b2 is not significant.