Regression analysis was individually applied between the dependent variable Y and three independent variables X₁, X₂ and X₃. The following estimated regression equations were obtained with 252 observations:

Model 1 = 100 + 10 X₁ R² = .70S_b1 = 30

Model 2 = 100 + 30 X₂ R² = .60S_b2 = 20

Model 3 = 100 - 30 X₃ R² = .80S_b3 = 10

For a level of significance of 5%:

a) Which variable can explain individually and statistically better the behaviour of Y?

b) Could the F test be useful in this case?

c) Can you predict the value of Y when X₁ = 10, X₂ = 10 and X₃ = 10 using any of the previous Models 1, 2 or 3?

Regression analysis was also applied between the dependent variable Y and two independent variables altogether X₃ and X₄. The following estimated regression equation was obtained with 43 observations:

Model 4 = 100 + 50 X₃ - 60 X₄

S_b3 = 10S_b4 = 10SSR = 90SSE = 10

For a level of significance of 1%:

d) Can you predict the value of Y when X₁ = 10, X₂ = 10, X₃ = 10 and X₄ = 10?

e) Would you change your two previous answers for a higher level of significance? Why?