A multiple regression model is to be constructed to predict the final exam score of a university student doing a particular course based upon their mid-term exam score, the average number of hours spent studying per week and the average number of hours spent watching television per week.

Data has been collected on 30 randomly selected individuals:show data

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37	68	9	28
25	43	2	10
37	56	4	21
61	70	18	35
45	65	17	35
41	39	16	26
21	31	17	18
33	22	20	26
50	69	5	19
45	47	12	15
40	63	16	27
70	88	17	8
30	35	13	5
20	35	7	11
60	82	5	6
22	30	12	33
48	56	14	19
44	48	14	23
46	71	18	22
38	68	9	29
46	82	9	17
46	54	20	7
43	55	6	26
48	52	17	25
17	32	8	9
41	68	2	30
72	99	17	20
28	41	19	27
49	80	6	25
43	51	20	7

a)Find the multiple regression equation using all three explanatory variables. Assume that X₁is mid-term score, X₂is hours studying per week and X₃is hours watching television per week. Give your answers to 3 decimal places.

y^=+mid-term score +hours studying +hours watching television

b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis

isis not

rejected.

For partsc)andd), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables.

c)The explanatory variable that is most correlated with final score is:

mid-term score hours studying per week hours watching television per week

d)The explanatory variable that is least correlated with final score is:

mid-term score hours studying per week hours watching television per week

e)The value of R²for this model, to 2 decimal places, is equal to

f)The value of s_efor this model, to 3 decimal places, is equal to

g)Construct a new multiple regression model by removing the variableaverage hours spent watching television per week. Give your answers to 3 decimal places.

The new regression model equation is:

y^=+mid-term score +hours studying

h)In the new model compared to the previous one, the value of R²(to 2 decimal places) is:

increased decreased unchanged

i)In the new model compared to the previous one, the value of s_e(to 3 decimal places) is:

increased decreased unchanged