Question

# A statistical program is recommended. Consider the following data for a dependent variable y and two...

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.

(b)

Develop an estimated regression equation relating y to

x2.

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

Predict y if

x2 = 16.

(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.

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

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