Question

The researcher wants to know if there is any relationship between resilience (higher scores equal higher rates of resilience) and optimism (higher scores equal higher levels of optimism).

Resilience scores (X)	Optimism scores (Y)
17.00 15.00 10.00 20.00 15.00 19.00	22.00 19.00 19.00 20.00 24.00 22.00

a. What is the Pearson’s correlation (r) between resilience and optimism?

b. Is the relationship positive or negative?

c. According to this data, what happens when a person has higher levels of optimism?

d. Plot the relationship between resilience and optimism on a scatterplot chart.

Answer 1

X	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
17 15 10 20 15 19	22 19 19 20 24 22	1.000 1.000 36.000 16.000 1.000 9.000 Sum: 64.000	1.000 4.000 4.000 1.000 9.000 1.000 Sum: 20.000	1.000 2.000 12.000 -4.000 -3.000 3.000 Sum: 11.000

1) correlation coefficient

X Values
∑ = 96
Mean = 16
∑(X - M_x)² = SS_x = 64

Y Values
∑ = 126
Mean = 21
∑(Y - M_y)² = SS_y = 20

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 11

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

r = 11 / √((64)(20)) = 0.3075

B) the relationship is postive

C) when person have higher levels of optimism then its act as an outlier whice gives incoorect direction of relationship between two variables.

D)