A multiple regression model is to be constructed to predict the final exam score

Question

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:

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 x3 is 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( is/is not )rejected.

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

A.mid-term score
B.hours studying per week
C.hours watching television per week

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

A.mid-term score
B.hours studying per week
C.hours watching television per week

e)The value of R2 for this model, to 3 decimal places, is equal to ___

f)The value of s 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 3 decimal places) is:

A.increased
B.decreased
C.unchanged

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

A.increased
B.decreased
C.unchanged

Final score Mid-term Score Hours studying
per week Hours watching TV
per week 34 22 15 8 77 94 17 30 68 69 16 29 55 68 2 5 61 61 17 27 47 29 16 15 65 90 3 19 55 53 12 25 42 36 12 8 39 32 18 32 64 83 1 16 40 54 5 25 66 74 9 18 25 35 3 23 34 44 6 25 74 72 17 14 55 55 11 9 53 68 2 17 58 75 9 32 50 43 12 31 26 26 15 29 38 41 11 14 31 21 18 21 75 90 4 27 64 68 14 9 78 95 5 20 75 80 15 34 49 73 3 22 32 39 6 13 53 38 19 20

Explanation / Answer

Regression Analysis: final score versus mid term score, hrs studying/wee, hrs watching TV/

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 3 6899.3 2299.77 114.54 0.000
mid term score 1 6770.4 6770.39 337.19 0.000
hrs studying/week 1 1156.9 1156.94 57.62 0.000
hrs watching TV/week 1 106.3 106.25 5.29 0.030
Error 26 522.0 20.08
Total 29 7421.4

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 1.46 3.55 0.41 0.684
mid term score 0.7574 0.0412 18.36 0.000 1.27
hrs studying/week 1.219 0.161 7.59 0.000 1.29
hrs watching TV/week -0.245 0.107 -2.30 0.030 1.12

a] Regression Equation

final score = 1.46 + 0.7574 mid term score + 1.219 hrs studying/week
- 0.245 hrs watching TV/week

b) At a level of significance of 0.05, the result of the F test =114.54

pvalue = 0.000 < alpha = 0.05

the null hypothesis is rejected.

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

Correlation: final score, mid term score

Pearson correlation of final score and mid term score = 0.880

A.mid-term score

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

Correlation: final score, hrs studying/week

Pearson correlation of final score and hrs studying/week = 0.001

B.hours studying per week

Model Summary

S R-sq R-sq(adj) R-sq(pred)
4.48092 92.97% 92.15% 90.38%

e)The value of R2 for this model = 0.9297

f)The value of s for this model = 4.4809

g) Regression Equation

final score = -1.06 + 0.7329 mid term score + 1.113 hrs studying/week

Model Summary

S R-sq R-sq(adj) R-sq(pred)
4.82392 91.53% 90.91% 89.01%

h)In the new model compared to the previous one, the value of R2 (to 3 decimal places) is:

B.decreased

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

A.increased

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