Compute the coefficients b_1 and b_2 for the regression model y_1 = b0 + b_1 x_1

Question

Compute the coefficients b_1 and b_2 for the regression model y_1 = b0 + b_1 x_1i + b_2 x_2i given the summary statistics shown below. a. r_x_1 y = 0.30, r_x_2 y = 0.80, r_x_1 x_2 = 0.20, s_x_1 = 400, s_x_2 = 300, s_y = 200 b. r_x_1 y = -0.30, r_x_2 y = -0.80, r_x_1 x_2 = 0.20, s_x_1 = 400, s_x_2 = 300, s_y = 200 c. r_x_1 y = 0.50, r_x_2 y = 0.15, r_x_1 x_2 = 0.90, s_x_1 = 400, s_x_2 = 300, s_y = 200 d. r_x_1 y = 0.30, r_x_2 y = 0.40, r_x_1 x_2 = 0.20, s_x_1 = 400, s_x_2 = 300, s_y = 200 a. b_1 = b_2 = b. b_1 = b_2 = c. b_1 = b_2 = d. b_1 = b_2 =

Explanation / Answer

answer

a)

b1 = rx1y × sy /sx1

=0.30*200/400

=0.15

b2=rx2y × sy /sx2

=0.80*200/300

=0.5333

b)

b1 = rx1y × sy /sx1

=-0.30*200/400

=-0.15

b2=rx2y × sy /sx2

=-0.8*200/300

=-0.5333

c)

b1 = rx1y × sy /sx1

=0.50*200/400

=0.25

b2=rx2y × sy /sx2

=0.15*200/300

=0.1

d)b1 = rx1y × sy /sx1

=0.30*200/400

=0.15

b2=rx2y × sy /sx2

=-0.40*200/300

=-02666

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