Y 

= 

a 

+ 

b X  

 straight 

line 

 Y 

= 

a 

+ 

b Log(X)      logarithmic 

curve 

 Log(Y) 

= 

a 

+ 

b X  

 exponential 

curve 

 Log(Y) 

= 

a 

+ 

b Log(X)      geometric 

curve 

 Y 

= 

a 

+ 

b 

X + 

c 

X2 parabola 

where X represents the independent variable and Y the dependent variable.  The constants a, b and c are 

calculated by the program using the method of least squares.  

The following statistics will be displayed in the results window: 

When you want to print these results, select the Print command in the Files menu, or press Ctrl+P. 

Results 

Sample size: the number of data pairs 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: 

 variation

explained

(Y

Y)

2

R

=

=

est

 variation

total

(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). 

Residual standard deviation: the standard deviation of the residuals (residuals = differences between 

observed and predicted values).  It is calculated as follows: 

(Y   Y )

2

est

s

=

res

2

n 

The residual standard deviation is sometimes called the Standard error of estimate (Spiegel, 1961). 

The equation of the regression curve: the selected equation with the calculated values for a and b (and 

for a parabola a third constant c), e.g.  Y  =  a  +  b X  

Next, the standard errors are given for the intercept (a) and the slope (b), followed by the t value and the 

P value for the hypothesis that these coefficients are equal to 0.  If the P values are low (e.g. less than 

0.05), then you can conclude that the coefficients are different from 0. 

57