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

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

(Y   Y )

2

s

=

est

res

1

k 

n 

The regression equation: the different regression coefficients bi with standard error sbi, t value and P 

value.  The P value is the probability that you would have found the current result if the coefficient were 

equal to 0 (null hypothesis).  If the P value for one or more coefficients is less than the conventional 0.05, 

then these coefficients can be called statistically significant, and the corresponding independent variables 

exert independent effects on the dependent variable Y 

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, and the multiple correlation coefficient can 

be called statistically significant. 

Zero order correlation coefficients: these are the simple correlation coefficients for the dependent 

variable Y and all independent variables Xi separately. 

Logistic regression 

Logistic regression is a technique for analyzing problems in which there are one or more independent 

variables that determine an outcome.  The outcome is measured with a dichotomous variable (in which 

there are only two possible outcomes). 

In logistic regression, the dependent variable is binary or dichotomous, 

i.e. it only contains data coded as 1 (TRUE, success, pregnant, etc. ) or 0 

(FALSE,  failure ,  non pregnant , etc.). 

The goal of logistic regression is to find the best fitting (yet biologically reasonable) model to describe the 

relationship between the dichotomous characteristic of interest (dependent variable = response or outcome 

variable) and a set of independent (predictor or explanatory) variables. Logistic regression generates the 

coefficients (and its standard errors and significance levels) of a formula to predict a logit transformation of 

the probability of presence of the characteristic of interest: 

b

=

logit(p)

b

+

X

0

1

1

b

+

2

X

2

b

+

3

X

3

b

+

. 

. 

.

+

k

X

k

where p is the probability of presence of the characteristic of interest. The logit transformation is defined as 

the logged odds: 

p

probabilit of

y 

of

presence

characteri

stic

=

odds

=

1  p

probabilit of

y 

of

absence

characteri

stic

and 

p

ln

=

logit(p)

1  p

Rather than choosing parameters that minimize the sum of squared errors (like in ordinary regression), 

estimation in logistic regression chooses parameters that maximize the likelihood of observing the sample 

values. 

The MedCalc dialog box for logistic regression is similar to the one for multiple regression (see p. 61).  In 

the dialog box you first identify the dependent variable.  Remember that the dependent variable must be 

binary or dichotomous, and it should only contain data coded as 0 or 1.  Cases with values other than 0 or 

1 for the dependent variable will be excluded from the analysis! 

63