Question

Q4. Professor Video, a college psychology instructor, wants to determine if there is a negative linear correlation between
a student’s GPA and the number of hours a student spends playing video games per week. She randomly selected twenty
students from all her classes and determined their number of hours playing video games per week and their GPA. The
sample results were:
GPA: 4.00 2.50 3.95 3.90 3.80 2.90 3.10 3.25 1.35 4.00
Hrs Playing: 0 15 3 5 0 13 8 7 12 10

GPA: 1.95 2.75 2.98 2.90 1.50 2.20 3.00 3.15 2.70 2.80
Hrs Playing: 12 13 11 10 17 9 6 8 13 16
(GPA SUMS: ∑X = 58.68 ∑X2 = 183.7054) (HRS SUMS: ∑X = 188 ∑X2 = 2214 )

d. Calculate the coefficient of determination & explain this result in terms of the dependent
and independent variable.
e. Write the Regression line equation for the relationship between a student’s GPA and the number of hours a
a student plays video games per week.
f. Use the Regression equation to predict the GPA of a student who plays 14 hours of video games
per week.

Answer 1

d) X - Hours Y - GPA

X Values
∑ = 188
Mean = 9.4
∑(X - M_x)² = SS_x = 446.8

Y Values
∑ = 58.68
Mean = 2.934
∑(Y - M_y)² = SS_y = 11.538

X and Y Combined
N = 20
∑(X - M_x)(Y - M_y) = -51.962

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -51.962 / √((446.8)(11.538)) = -0.7237

The value of R², the coefficient of determination, is 0.5237.

R² value is really low. Hours playing videogames and GPA are weakly correlated.

e) X - Hours Y - GPA

Sum of X = 188
Sum of Y = 58.68
Mean X = 9.4
Mean Y = 2.934
Sum of squares (SS_X) = 446.8
Sum of products (SP) = -51.962

Regression Equation = y = bX + a

b = SP/SS_X = -51.96/446.8 = -0.1163

a = M_Y - bM_X = 2.93 - (-0.12*9.4) = 4.0272

y = -0.1163X + 4.0272

f) For 14 hours paying x = 14

so y = -0.1163*14 + 4.0272 = 2.399

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