Question

Q1. Using the data provided for your group assignment estimate the simple regression

Y= Final_exam and X= assignment_grade. Each part of question is worth 2 marks.

1. Prior to estimating the regression what are your a priori expectations about the sign of β1? Explain.
2. Write down the regression results in traditional form, with t statistics below each of the estimated coefficients and anything else that should be included.
3. Test the null hypothesis that β1=0 against the two sided alternative hypothesis at the 5% level of significance. Interpret your results.
4. Now estimate the multiple regression model including assignment_grade (X1) and Tutorial_attend (X2). Write down the regression results in traditional form, with t statistics below each of the estimated coefficients and anything else that should be included.
5. Within the multiple regression model- test the null hypothesis that β1=0 against the two sided alternative hypothesis at the 5% level of significance. Interpret your results.

Final_exam	assignment_grade	Tutorial_attend
100	90	5
100	75	5
90	75	5
85	85	5
85	100	5
80	95	5
70	80	5
60	95	5
60	80	5
55	95	5
55	25	4
50	80	5
45	90	5
40	65	5
40	65	4
35	0	3
30	70	4
30	55	4
25	85	5
25	90	4
15	5	3
15	80	5
15	50	5
15	45	3
5	75	3
5	70	4
100	100	5
95	75	5
90	100	5
85	85	5
80	95	5
70	45	5
70	100	5
65	90	5
60	100	5
55	65	4
55	90	5
55	80	4
50	50	5
45	50	4
45	75	3
40	75	5
40	70	5
35	90	4
30	95	5
30	55	5
25	75	4
25	20	3
25	65	2
15	60	4
15	60	4
15	80	5
10	55	4
10	80	2
0	0	2

Answer 1

Answer(i):

Here we have Final_exam score as dependent variable and assignment grade as independent variable. Our expectation will be of a positive relationship between the dependent and independent variable as generally the final _exam score will increase with the increase in assignment grade.

Hence our expectation of sign of β1 is Positive.

Answer(ii):

We used excel data analysis tool to fit a simple regression model and the output in the tradition from is given below:

	Intercept	Assignment_grade
Coefficients	8.556 (10.349)	0.537 (0.138)
t statistic	0.827	3.896

*values in parentheses are standard errors

The fitted regression equation is

Answer(iii):

We have to test

H0: β1 = 0

H1: β1 ≠ 0

we have the t statistic for β1

­t=3.896

The critical value of t for two tailed alternative hypothesis at 0.05 level of significance with 53df is 2.005

The t statistic for β1 is 3.896 which is greater than tcritical = 2.005 and it suggest that we have enough evidence against H0 to reject it, so we reject the H0 at 5% level of significance and conclude that the β1 is highly significant.

Answer(iv):

We used excel data analysis tool to fit a multiple regression model and the output in the tradition from is given below:

	Intercept	assignment_grade	Tutorial_attend
Coefficients	-35.753 (15.549)	0.218 (0.153)	15.338 (4.296)
t statistic	-2.300	1.421	3.570

*values in parentheses are standard errors

The fitted regression equation is

Answer(v):

We have to test

H0: β1 = 0

H1: β1 ≠ 0

we have the t statistic for β1

­t=1.421

The critical value of t for two tailed alternative hypothesis at 0.05 level of significance with 53df is 2.005

The t statistic for β1 is 3.896 which is less than tcritical = 2.005 and it suggest that we do not have enough evidence against H0 to reject it, so we fail to reject the H0 at 5% level of significance and conclude that the β1 is not significant.