Question

y	10	11	15	15	20	24	27	32
x1	2	5	5	9	7	11	16	20
x2	16	10	13	10	2	8	7	4

Construct a? 95% confidence interval for the dependent variable when x1=9 and x2=14?

The 95% prediction interval for the dependent varible when x1=9 and x2=14?

Answer 1

Using MINITAB

Choose Stat > Regression > Regression.

In Response, enter Y.

In Predictors, enter x1 x2.

click on option

go to predictor interval and put the values x1 = 9 and x2 = 14

confidence level = 95

select the check box of Confidence limits and Prediction limits

click ok

Session window output

MTB > Regress 'Y' 2 'X1' 'X2';
SUBC>   Constant;
SUBC>   Predict 9 14;
SUBC>     CLimits 'CLIM1'-'CLIM2';
SUBC>     PLimits 'PLIM1'-'PLIM2';
SUBC>   Brief 1.

Regression Analysis: Y versus X1, X2

The regression equation is
Y = 12.3 + 1.06 X1 - 0.347 X2

Predictor     Coef     SE Coef      T      P
Constant    12.338    4.229    2.92 0.033
X1         1.0615   0.2159   4.92 0.004
X2        -0.3474   0.2875 -1.21 0.281

S = 2.64526   R-Sq = 92.0%   R-Sq(adj) = 88.8%

Analysis of Variance

Source            DF      SS      MS        F      P
Regression       2     400.51 200.26 28.62 0.002
Residual Error   5 34.99    7.00
Total              7 435.50

Predicted Values for New Observations

New Obs     Fit         SE Fit        95% CI          95% PI
      1          17.028   1.732        (12.575, 21.481) (8.900, 25.156)

Values of Predictors for New Observations

New Obs    X1    X2
      1    9.00 14.0