Calculate the linear regression equation for each of these situations:

a. Variable \(X\) : Range \(=1-6, \bar{X}_{i}=5.00, s_{X}=2.00\); Variable \(Y\) : Range \(=1-6, \bar{Y}=4.00, s_{Y}=1.00\), Correlation: \(r=.40\)

b. Variable \(X\) : Range \(=0-6, \bar{X}_{i}=3.59, s_{X}=1.32\); Variable \(Y\) : Range \(=1-10, \bar{Y}=7.52, s_{Y}=2.46\), Correlation: \(r=-.28\)

c. Variable \(X\) : Range \(=0-100, \bar{X}_{i}=73.87, s_{X}=12.65\); Variable \(Y\) : Range \(=0-125, \bar{Y}=86.32, s_{Y}=16.80\), Correlation: \(r=.07\)

d. Variable \(X\) : Range \(=1-20, \bar{X}_{i}=14.41, s_{X}=2.09\); Variable \(Y\) : Range \(=1-50, \bar{Y}=37.88, s_{Y}=6.23\), Correlation: \(r=-.51\)

e. Variable \(X\) : Range \(=0-250, \bar{X}_{i}=134.91, s_{X}=25.96\); Variable \(Y\) : Range \(=0-250, \bar{Y}=179.33, s_{Y}=21.63\), Correlation: \(r=.34\)