Note that when you use the regression equation for prediction, you may only apply it to values in the range 

of the actual observations.  E.g. when you have calculated the regression equation for height and weight 

for school children, this equation cannot be applied to adults. 

Analysis of variance: the analysis of variance table divides the total variation in the dependent variable 

into two components, one which can be attributed to the regression model (labeled Regression) and one 

which cannot (labeled Residual).  If the significance level for the F test is small (less than 0.05), then the 

hypothesis that there is no (linear) relationship can be rejected. 

Presentation of results 

If the analysis shows that the relationship between the two variables is too weak to be of practical help, 

then there is little point in quoting the equation of the fitted line or curve.  If you give the equation, you also 

report the standard error of the slope, together with the corresponding P value.  Also the residual standard 

deviation should be reported (Altman, 1980).  The number of decimal places of the regression coefficients 

should correspond to the precision of the raw data.   

The accompanying scatter diagram should include the fitted regression line when this is appropriate.  This 

figure can also include the 95% confidence interval, or the 95% prediction interval, which can be more 

informative, or both.  The legend of the figure must clearly identify the interval that is represented. 

Scatter diagram & Regression line 

In a scatter diagram, the relation between two numerical variables is presented graphically.  One variable 

(the independent variable X) defines the horizontal axis and the other (dependent variable Y) defines the 

vertical axis.  The values of the two variables on the same row in the data spreadsheet, give the points in 

the diagram. 

The dialog box for the scatter diagram is similar to the one for Regression (see p. 56): 

The regression curve will be drawn in the diagram.  The equation of this curve is given in the Regression 

results window. When you select an equation that contains a logarithmic transformation for one or both of 

the variables, the program will use a logarithmic scale for the corresponding variable(s). 

Finally, you can select 2 options: 

95% Confidence: when you select this option then two curves will be drawn parallel to the regression line.  

These curves represent a 95% confidence interval for the regression line.  This interval includes the true 

regression line with 95% probability. 

95% Prediction: when you select this option then two curves will be drawn parallel to the regression lines.  

These curves represent the 95% prediction interval for the regression curve.  The 95% prediction interval 

is much wider than the 95% confidence interval.  For any given value of the independent variable, this 

interval represents the 95% probability for the values of the dependent variable. 

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