Question

A statistical program is recommended.

Consider the following data for a dependent variable y and two independent variables,

x₁

and

x₂.

x1	x2	y
30	12	94
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	211

(a)

Develop an estimated regression equation relating y to

x₁.

(Round your numerical values to one decimal place.)ŷ =

  Predict y if

x₁ = 51.

(Round your answer to one decimal place.)

(b)

Develop an estimated regression equation relating y to

x₂.

(Round your numerical values to one decimal place.)ŷ =

  Predict y if

x₂ = 16.

(Round your answer to one decimal place.)

(c)

Develop an estimated regression equation relating y to

x₁ and x₂.

(Round your numerical values to one decimal place.)ŷ =

  Predict y if

x₁ = 51

and

x₂ = 16.

(Round your answer to one decimal place.)

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put y in Y input range and put x1, x2 and then x1 and x2 in X input range seperately and run 3 seperate models.

a) x1

	Coefficients	Standard Error	t Stat	P-value
Intercept	51.53	18.14	2.84	0.02
x1	-0.21	1.35	-0.15	0.88

y = 51.53 - 0.21x1

x₁ = 51, y = 51.53 - 0.21*51 = 40.8

b) x2

	Coefficients	Standard Error	t Stat	P-value
Intercept	1.32	12.53	0.11	0.92
x2	0.34	0.09	3.94	0.00

y = 1.32 - 0.34x₂

x₂ = 16, y = 1.32 - 0.34*16 = -4.1

c) x1 and x2

	Coefficients	Standard Error	t Stat	P-value
Intercept	13.19	7.63	1.73	0.13
x1	-2.15	0.51	-4.24	0.00
x2	0.45	0.06	8.13	0.00

y = 13.19 - 2.15x₁ + 0.45x₂

x₁ = 51 and x₂ = 16, 13.19 - 2.15*51+ 0.45*16 = 13.19 - 116.85 = -103.66