A mathematics placement test is given to all entering freshmen at Eastern
University. n = 55, ̄x = 4, ̄y = 12, ∑\sum∑ni=1 xi2=232, ∑\sum∑ni=1 xiyi=318 .Fit a simple
linear regression model between x and y
Regression equation: y=a+bx.y=a+bx.y=a+bx.
b=ΣxyΣx2=318232=1.3707.b=\frac{\Sigma xy}{\Sigma x^2}= \frac{318}{232}=1.3707.b=Σx2Σxy=232318=1.3707.
a=yˉ−bxˉ=12−1.3707∗4=6.5172.a=\bar y-b\bar x=12-1.3707*4=6.5172.a=yˉ−bxˉ=12−1.3707∗4=6.5172.
Thus, the regression equation is y=6.5172+1.3797x.y=6.5172+1.3797x.y=6.5172+1.3797x.
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