Polynomial Regression

• Creating the x-squared terms
• Getting Slope, Y Intercept and Model Utility Test
• Confidence Interval for  average y and Prediction Interval for next y

Creating the x-squared terms

• This step happens before you do run the regression. Go to Calc, Calculator. The following screen will appear.

• Enter the column that you want to store the data in the first box.
• Enter thecalculation in the Expression box.
• If you want to square the x term, it is probably easiest to just double-click on the variable name

hit the "*" key on the pad and then hit the variable again.
• Hit o.k.
• The column that you listed in the first box will have the transformed data.

Getting Slope, Y Intercept and Model Utility Test

• Enter your data. X should be in one column and Y should be in the next column.
• Go to Stat, Regression, Regression. The following screen should appear.

• Enter your Y variable as your response. Enter your X and Xsquared  variable as your predictor. Click on o.k.
• The following output should appear.

 
Regression Analysis: y versus x, xsquared
 

The regression equation is
y = 84.5 - 15.9 x + 1.77 xsquared

Predictor        Coef     SE Coef          T        P
Constant       84.482       4.904      17.23    0.000
x             -15.875       2.500      -6.35    0.001
xsquared       1.7679      0.2712       6.52    0.001

S = 3.515       R-Sq = 89.5%     R-Sq(adj) = 85.3%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         2      525.11      262.55     21.25    0.004
Residual Error     5       61.77       12.35
Total              7      586.87

Source       DF      Seq SS
x             1        0.05
xsquared      1      525.05

Confidence Interval for  average y and Prediction Interval for next y

• Follow the steps above but before you hit o.k. Go to options. The following screen should appear.

• In the box for Prediction Intervals for new observations, enter your new x and the x-squared term. As shown below, if x=2, then you have to enter 2 "space" 4.
• If you want to change your condifence, enter that as well in the box below.
• Click O.K.
• Additional lines will be added to your output. It should look similar to the following output below.
• This will give you both the confidence interval and the prediction interval.

Predicted Values for New Observations

New Obs     Fit     SE Fit         95.0% CI             95.0% PI
1         59.80       1.86   (   55.02,   64.58)  (   49.58,   70.03)