Question

The following data for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling:

X	Y
10	120
14	130
16	170
12	150
20	200
18	180
16	190
14	150
16	160
18	200

1. Construct a scatter plot for these data. Based on the scatter plot, how would you describe the relationship between the two variables?
2. Compute the correlation coefficient.

Answer 1

a) Based on the given data the scatter plot is plotted as:

Based on the scatter plot data distribution we can say that there is a strong positive correlation between the variables.

b) To calculate the correlation coefficient following table calculation is cone as:

X Values
∑ = 154
Mean = 15.4
∑(X - M_x)² = SS_x = 80.4

Y Values
∑ = 1650
Mean = 165
∑(Y - M_y)² = SS_y = 7050

X and Y Combined
N = 10
∑(X - M_x)(Y - M_y) = 670

Where,

X: X Values
Y: Y Values
M_x: Mean of X Values
M_y: Mean of Y Values
X - M_x & Y - M_y: Deviation scores
(X - M_x)² & (Y - M_y)²: Deviation Squared
(X - M_x)(Y - M_y): Product of Deviation Scores

Now the correlation is calculated as:

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

r = 670 / √((80.4)(7050)) = 0.8899

The 0.89 correlation explains that there is strong correlation between the two variables.