Question

Consider the following table containing unemployment rates for a 10-year period.

Unemployment Rates

Year	Unemployment Rate (%)
1	3.5
2	5.2
3	7.8
4	8.1
5	3.7
6	9.6
7	8.7
8	3.5
9	11.1
10	8.8

What is the coefficient of determination for the regression model? Round your answers to two decimal places.

Answer 1

The coefficient of determination= r²

Now,

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

X Values
∑ = 55
Mean = 5.5
∑(X - M_x)² = SS_x = 82.5

Y Values
∑ = 70
Mean = 7
∑(Y - M_y)² = SS_y = 70.18

X and Y Combined
N = 10
∑(X - M_x)(Y - M_y) = 37.6

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

r = 37.6 / √((82.5)(70.18)) = 0.4941

The value of R², the coefficient of determination, =r² = 0.24