Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

ŷ = 18.9 + 3.2x₁ − 2.2x₂ + 7.8x₃ + 2.9x₄

(a)

Interpret

b₁

in this estimated regression equation.

b₁ = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x₃ when x₁, x₂, and x₄ are held constant.b₁ = 3.2 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂, x₃, and x₄ are held constant.    b₁ = 3.2 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁, x₃, and x₄ are held constant.b₁ = −2.2 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂, x₃, and x₄ are held constant.b₁ = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x₄ when x₁, x₂, and x₃ are held constant.

Interpret

b₂

in this estimated regression equation.

b₂ = −2.2 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂, x₃, and x₄ are held constant.b₂ = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x₃ when x₁, x₂, and x₄ are held constant.    b₂ = −2.2 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁, x₃, and x₄ are held constant.b₂ = 3.2 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂, x₃, and x₄ are held constant.b₂ = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x₄ when x₁, x₂, and x₃ are held constant.

Interpret

b₃

in this estimated regression equation.

b₃ = 3.2 is an estimate of the change in y corresponding to a 1 unit change in x₃ when x₁, x₂, and x₄ are held constant.b₃ = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁, x₃, and x₄ are held constant.    b₃ = −2.2 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂, x₃, and x₄ are held constant.b₃ = −2.9 is an estimate of the change in y corresponding to a 1 unit change in x₄ when x₁, x₂, and x₃ are held constant.b₃ = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x₃ when x₁, x₂, and x₄ are held constant.

Interpret

b₄

in this estimated regression equation.

b₄ = −2.2 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁, x₃, and x₄ are held constant.b₄ = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x₃ when x₁, x₂, and x₄ are held constant.    b₄ = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x₄ when x₁, x₂, and x₃ are held constant.b₄ = 7.8 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁, x₃, and x₃ are held constant.b₄ = 3.2 is an estimate of the change in y corresponding to a 1 unit change in x₄ when x₁, x₂, and x₃ are held constant.

(b)

Predict y when

x₁ = 10, x₂ = 5, x₃ = 1, and x₄ = 2.

Answer 1