Use computer software packages, such as Minitab or Excel, to solve this problem.

ID: 3156566 • Letter: U

Question

Consider the following data for a dependent variable y and two independent variables, x1 and x2.

The estimated regression equation for this data is

= -18.1+ 1.97x1 + 4.68x2

Round your answers to two decimal places.

a. Develop a 95% confidence interval for the mean value of y when x1 = 45 and x2 = 15.

95% confidence interval is to .

b. Develop a 95% prediction interval for y when x1 = 45 and x2 = 15.

95% prediction interval is to .

x1 x2 y 29 12 94 46 10 109 24 18 113 51 16 179 40 6 95 52 20 176 74 8 170 37 13 117 59 14 142 77 16 211

Below is the output from minitab.

Regression Analysis: y versus x1, x2

The regression equation is
y = 1.81 x1 + 3.98 x2

Predictor Coef SE Coef T P
Noconstant
x1 1.8097 0.1757 10.30 0.000
x2 3.9833 0.6509 6.12 0.000

S = 12.6588

Analysis of Variance

Source DF SS MS F P
Regression 2 211520 105760 659.99 0.000
Residual Error 8 1282 160
Total 10 212802

Source DF Seq SS
x1 1 205519
x2 1 6001

Predicted Values for New Observations

New
Obs Fit SE Fit 95% CI 95% PI
1 141.19 4.39 (131.06, 151.31) (110.29, 172.08)

Values of Predictors for New Observations

New
Obs x1 x2
1 45.0 15.0

[ANSWERS

a. (131.06, 151.31)

b. (110.29, 172.08)

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