Use computer software packages, such as Minitab or Excel, to solve this problem.
ID: 3260326 • Letter: U
Question
Use computer software packages, such as Minitab or Excel, to solve this problem.
Consider the following data for a dependent variable y and two independent variables, x1 and x2.
The estimated regression equation for this data is
= -14.7+ 1.9x1 + 4.66x2
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 95 46 11 109 24 18 113 50 16 179 41 5 94 51 20 176 75 8 170 37 13 118 60 14 143 76 17 211Explanation / Answer
using minitab:
Step 1) First enter the given data set in minitab columns.
Step 2) Click on Stat>>>Regression>>>General regression...
Response: select y
Model: select x1 and x2
Step 3) Click on Prediction
in "New observation for continuous predictors:
we want to predict y for given x1 = 45 and x2 = 15
So put 45 then space and then put 15
Select confidence limits:
and prediction limits
Then click on OK
then click on Option.
Confidence level for all interval: put 95
Types of confidence interval: Two-sided.
then click on OK and again Click on OK
So we get the following minitab output
General Regression Analysis: y versus x1, x2
Regression Equation
y = -14.7149 + 1.9024 x1 + 4.66325 x2
Coefficients
Term Coef SE Coef T P
Constant -14.7149 19.5837 -0.75139 0.477
x1 1.9024 0.2653 7.17190 0.000
x2 4.6632 1.0070 4.63080 0.002
Summary of Model
S = 13.9573 R-Sq = 90.95% R-Sq(adj) = 88.37%
PRESS = 2051.85 R-Sq(pred) = 86.39%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 2 13712.0 13712.0 6856.0 35.1937 0.0002226
x1 1 9534.5 10020.1 10020.1 51.4361 0.0001819
x2 1 4177.5 4177.5 4177.5 21.4443 0.0023954
Error 7 1363.6 1363.6 194.8
Total 9 15075.6
Fits and Diagnostics for Unusual Observations
No unusual observations
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 140.842 4.79754 (129.497, 152.186) (105.943, 175.741)
Values of Predictors for New Observations
New Obs x1 x2
1 45 15
From the above output
a) The 95% confidence interval for the mean value of y when x1 = 45 and x2 = 15 is (129.497, 152.186)
b) The 95% prediction interval for y when x1 = 45 and x2 = 15 is (105.943, 175.741)
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