Question

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

University. n = 55,  ̄x = 4, ̄y = 12, $\sum$ⁿ_i=1 x_i²=232, $\sum$ⁿ_i=1 x_iy_i=318 .Fit a simple

linear regression model between x and y

Answer 1

Regression equation: $y=a+bx.$

$b=\frac{\Sigma xy}{\Sigma x^2}= \frac{318}{232}=1.3707.$

$a=\bar y-b\bar x=12-1.3707*4=6.5172.$

Thus, the regression equation is $y=6.5172+1.3797x.$