Simple Linear Regression

• Getting Slope, Y Intercept and Model Utility Test
• Predicting average y and next y
• Making Residual Plots
• Transforming the x's and y's

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 variable as your predictor. Click on o.k.
• The following output should appear.

Regression Analysis: height versus age

The regression equation is
height = 72.0 + 0.383 age

Predictor        Coef     SE Coef          T        P
Constant       71.950       1.053      68.33    0.000
age           0.38333     0.02041      18.78    0.000

S = 0.3873      R-Sq = 98.9%     R-Sq(adj) = 98.6%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1      52.900      52.900    352.67    0.000
Residual Error     4       0.600       0.150
Total              5      53.500

Predicting New 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.
• 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.

Predicted Values for New Observations

New Obs     Fit        SE Fit           95.0% CI             95.0% PI
1              84.600      0.400      (  83.489,  85.711)  (  83.054,  86.146) X
X  denotes a row with X values away from the center

Values of Predictors for New Observations

New  Obs       age
1                     33.0

• This will give you both the confidence interval and the prediction interval.

Making Residual Plots

• Follow the instructions above but before you hit o.k., go to Graphs. The following screen should appear.

• Click on the options as displayed above. You want a histogram of residuals, the normal probability plot and the residual plot that is (residuals vs. x).
• Click on o.k. The following plots should appear.

Note: This graphs are a little off because n=6. For a better regression equation, use more points.

Transforming the x's and y's

• 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 the transformation in the Expression box.
• It is a good idea to use the scroll screen on the side to select the exact code needed to do that transformation.
• Enter the variable that you are conducting the transformation on inside the parenthesis.
• Hit o.k.
• The column that you listed in the first box will have the transformed data.