Question

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

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.612917385
R Square	0.375667721
Adjusted R Square	0.351654941
Standard Error	22.82783542
Observations	55
ANOVA
	df	SS	MS	F	Significance F
Regression	2	16305.00365	8152.501823	15.64449105	4.79524E-06
Residual	52	27097.72363	521.1100697
Total	54	43402.72727
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-35.7528379	15.54695813	-2.299667729	0.025513459	-66.95009176	-4.555584041	-66.95009176	-4.555584041
assignment_grade	0.218051561	0.153416203	1.421307252	0.161197169	-0.089800572	0.525903695	-0.089800572	0.525903695
Tutorial_attend	15.33752081	4.29606168	3.570135151	0.000778134	6.716842368	23.95819925	6.716842368	23.95819925

7. Using your multiple regression results to predict Final_exam for a student with the mean assignment_grade and tutorial_attend equal to (i) 2 tutorials, (ii) 3, (iii) 4 and (iv) 5 tutorials. (Hint this means you will have 4 distinct predictions for Final_exam) Carefully interpret your results.

Answer 1

In order to predict finall exaam score we need value of assignment grade and tutorial attend. Here you provide values for tutorial attend. So we cant predict the finall exaam score.

We can only predict the effect of tutorial attended on finall exaam score.

i. For 2 tutorials:

Finall exaam score is on an average increased by 15.34 * 2= 30.68 if a student attend 2 tutorials while the assignment grades are keep constant.

ii. For 3 tutorials:

Finall exaam score is on an average increased by 15.34 * 3= 46.02  if a student attend 3 tutorials while the assignment grades are keep constant.

iii. For 4 tutorials:

Finall exaam score is on an average increased by 15.34 * 4= 61.36 if a student attend 4 tutorials while the assignment grades are keep constant.

iv. For 5 tutorials:

Finall exaam score is on an average increased by 15.34 * 5 = 76.7 if a student attend 5 tutorials while the assignment grades are keep constant.