Results 

If you want to repeat the Multiple regression procedure, possibly to add or remove variables in the model, 

then you only have to press function key F7.  The dialog box will re appear with the previous entries (see p. 

14). 

In the results window, the following statistics are displayed: 

Sample size: the number of data records n 

Coefficient of determination: this is the proportion of the variation in the dependent variable explained by 

the regression model, and is a measure of the goodness of fit of the model.  It can range from 0 to 1, and 

is calculated as follows: 

explained variation

(Y

Y)

2

R

=

=

est

total variation

(Y

Y)

2

where 

Y

 are the observed values for the dependent variable, 

Y

 is the average of the observed values and 

Yest

 are predicted values for the dependent variable (the predicted values are calculated using the 

regression equation). 

R adjusted: this is the coefficient of determination adjusted for the number of independent variables in the 

regression model. Unlike the coefficient of determination, R adjusted may decrease if variables are entered 

in the model that do not add significantly to the model fit.  

unexplained variation

 /

k

(n

1)

R

1

=

adj

total variation

 /

1)

(n

or 

Y

(Y

)

2

est

1)

(n 

R

1

=

adj

(Y

Y)

2

1)

k 

(n 

Multiple correlation coefficient: this coefficient is a measure of how tightly the data points cluster around 

the regression plane, and is calculated by taking the square root of the coefficient of determination. 

When discussing multiple regression analysis results, generally the coefficient of multiple determination is 

used rather than the multiple correlation coefficient. 

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