Question

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

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.

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