Question

MGMT 582

Homework: Validation Problem

Pearson’s r

1. Given the following table answer the questions.

Respondent	Score X	Score Y	X – x̄	(X – x̄) ²	Y – ȳ	(Y – ȳ) ²	(X – x̄) (Y– ȳ)
Rose	18	92
Bush	36	65
Novicevic	24	91
Vitell	28	85
Walker	25	70

1. Calculate Pearson’s Product Movement Correlation Coefficient (r). Show your work.
2. Based on the correlation coefficient which you calculated, in two words how would you describe the relationship between the two variables in the “test”?

2. PHR Score

Respondent	Score X	Score Y	X – x̄	(X – x̄) ²	Y – ȳ	(Y – ȳ) ²	(X – x̄) (Y– ȳ)
Selber	96	92
Franklin	56	65
Nichols	84	91
Vitello	88	85
Grado	72	70

1. Calculate Pearson’s Product Movement Correlation Coefficient (r). Show your work.
2. Based on the correlation coefficient which you calculated, in two words how would you describe the relationship between the two variables in the “test”?

3. Which of the two “tests” above would you choose? Why?

Answer 1

1.

X Values
∑ = 131
Mean = 26.2
∑(X - Mx)2 = SSx = 172.8

Y Values
∑ = 403
Mean = 80.6
∑(Y - My)2 = SSy = 613.2

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -248.6

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -248.6 / √((172.8)(613.2)) = -0.7637

b. As r is negative and value is near 1, so it is strong negative correlation

2.

X Values
∑ = 396
Mean = 79.2
∑(X - Mx)2 = SSx = 972.8

Y Values
∑ = 403
Mean = 80.6
∑(Y - My)2 = SSy = 613.2

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 718.4

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 718.4 / √((972.8)(613.2)) = 0.9302

b. As r is positive and value is near 1, there is strong postivie correlation