The linear regression of the set of data is y = 0.13x + 1.75 and the correlation coefficient is 0.2604
Finding the linear regression of the set of data
From the question, we have the following parameters that can be used in our computation:
X 1, 2, 3, 4, 5
y 1.5 2.6 1.5 3.3 1.8
Using a graphing tool, we have the following summary
- Sum of X = 15
- Sum of Y = 10.7
- Mean X = 3
- Mean Y = 2.14
- Sum of squares (SSX) = 10
- Sum of products (SP) = 1.3
The regression equation is represented as
y = bx + a
Where
b = SP/SSx = 1.3/10 = 0.13
a = My - bMx = 2.14 - (0.13*3) = 1.75
So, we have
y = 0.13x + 1.75
For the correlation coefficient, we have the following summary
x values
∑ = 15
Mean = 3
∑(X - Mx)² = SSx = 10
y values
∑ = 10.7
Mean = 2.14
∑(Y - My)² = SSy = 2.492
x and y Combined
n = 5
∑(X - Mx)(Y - My) = 1.3
r Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
So, we have
r = 1.3 / √((10)(2.492))
Evaluate
r = 0.2604
Hence, the correlation coefficient is 0.2604