With this set of data incarceration rate dependent variable

Solution

Let Y=incarceration rate, X₁=median income, X₂=Total crime

We now model them as-

Y=a+b₁X₁+b₂X₂+e

We now estimate a,b₁,b₂ by the method of least squares by minimizing the term e².

where e_i=Y_i-a-b₁X_1i+b₂X_2i,

Now from the data we estimate them as- a=1028, b₁=-0.0142, b₂=0.139

Therefore,the least square line is given by-

Y=1028 - 0.0142X₁ + 0.139X₂

Now the co-efficient of determination,R²=0.596

Pearson\'s r = cov(X,Y)/SxSy

r(Y,X₁)=-0.732

r(Y,X₂)=0.701

r(X₁,X₂)=-0.726