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

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

  1. Enter the column that you want to store the data in the Store Result in variable box.
  2. Enter the calculation in the Expression box.
  3. If you want to square the x term, it is probably easiest to just double-click on the variable name, then
    hit the "*" key on the pad and then hit the variable again.
  4. Hit o.k.
  5. The column that you listed in the first box will have the transformed data.


Getting Slope, Y Intercept and Model Utility Test

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

  1. Enter your Y variable as your Response. Enter your X and Xsquared variable as your Predictors. Click on o.k.
  2. The following output should appear.

Regression Analysis: Score2 versus Score1, Score1squared

 

The regression equation is

Score2 = 1.06 + 0.241 Score1 - 0.0021 Score1squared

 

 

Predictor          Coef  SE Coef      T      P

Constant         1.0640   0.3202   3.32  0.016

Score1           0.2412   0.1315   1.83  0.116

Score1squared  -0.00209  0.01155  -0.18  0.863

 

 

S = 0.137256   R-Sq = 95.7%   R-Sq(adj) = 94.3%

 

 

Analysis of Variance

 

Source          DF      SS      MS      F      P

Regression       2  2.5425  1.2713  67.48  0.000

Residual Error   6  0.1130  0.0188

Total            8  2.6556

 

Notice that in this case, the p-value for the squared term is very high. This means that there is not sufficient evidence that the Beta2 (the slope term for the squared term) is sufficiently different from zero. The regression should be rerun without the squared term.

Confidence Interval for average y and Prediction Interval for next y

  1. Follow the steps above but before you hit o.k., go to options. The following screen should appear.

 

  1. 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.
  2. If you want to change your confidence, enter that as well in the box below.
  3. Click O.K.
  4. 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% CI            95% PI

  1  1.5380  0.1188  (1.2473, 1.8287)  (1.0938, 1.9822)

 

 

Values of Predictors for New Observations

 

New

Obs  Score1  Score1squared

  1    2.00           4.00