Question

A mathematics placement test is given to all entering freshmen at Eastern

University. n = 58,x ̄= 4,y ̄ = 12, ∑ⁿ_i=1 x_i² =232, ∑ⁿ_i=1 x_iy_i =318. , .Fit a simple

linear regression model between x and y.

Answer 1

$n = 58 \\ \bar{x} = 4 \\ \bar{y} = 12 \\ x_i = X_i - \bar{x} \\ y_i = Y_i - \bar{y} \\ y = β_1 + β_2x \\ β_2 = \frac{\sum x_iy_i}{\sum x_i^2} \\ = \frac{318}{232} = 1.37 \\ β_1 = y - β_2x \\ = 12 - (1.37 \times 4) \\ = 6.52$

The simple linear regression model between x and y:

y = 6.52 + 1.37x