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[answered] A multiple regression model is to be constructed to predict


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

Download the data

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 X1?is mid-term score, X2?is 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 parts?c)?and?d), 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 R2?for this model, to 2 decimal places, is equal to?

f)The value of se?for this model, to 3 decimal places, is equal to?

g)Construct a new multiple regression model by removing the variable?average 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 se?(to 3 decimal places) is:

increased
decreased
unchanged


 


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