Calculate the linear regression equation for each of these situations:

a. Variable \(X\) : Range \(=0-60, \bar{X}_{i}=45.00, s_{X}=5.00\); Variable \(Y\) : Range \(=0-25, \bar{Y}=11.00, s_{Y}=3.00\), Correlation: \(r=.30\)

b. Variable \(X\) : Range \(=0-100, \bar{X}_{i}=37.22, s_{X}=11.76\); Variable \(Y\) : Range \(=0-150, \bar{Y}=104.32, s_{Y}=15.92\) Correlation: \(r=.62\)

c. Variable \(X\) : Range \(=1-6, \bar{X}_{i}=4.32, s_{X}=.97\); Variable \(Y\) : Range \(=1-5, \bar{Y}=2.51, s_{Y}=.46\), Correlation: \(r=-.09\)

d. Variable \(X\) : Range \(=1-5, \bar{X}_{i}=3.91, s_{X}=1.04\); Variable \(Y\) : Range \(=1-110, \bar{Y}=76.40, s_{Y}=9.87\), Correlation: \(r=.25\)

e. Variable \(X\) : Range \(=1-12, \bar{X}_{i}=8.75, s_{X}=1.78\); Variable \(Y:\) Range \(=0-35, \bar{Y}=24.65, s_{Y}=4.82\), Correlation: \(r=-.54\)