For continuous
independent variables, the
b coefficient indicates the change in the dependent variable per unit change in
the independent variable, **controlling for the confounding effects of the
other independent variables in the model. ** A discrete random variable, X_{1},
can assume 2 or more distinct values corresponding to the number of subgroups in
a given category. For example, in the gender category there are 2 subgroups,
men (X_{i }=1) and women (X_{i }= 2). One subgroup
(usually arbitrarily) is designated as the reference group. The beta
coefficient for a discrete variable indicates the difference in the dependent
variable for one value of X_{i }, (e.g., the difference between women and the
reference group, men), when all other independent variables in the model are held
constant. A positive value for the beta coefficient indicates a larger value of the dependent variable for the
subgroup (women) than for the reference group (men), whereas a
negative value for the beta coefficient indicates a smaller value.

** **

Independent variable type |
Examples |
What does the b coefficient mean in Simple linear regression? |
What does the b coefficient mean in Multiple linear regression? |
---|---|---|---|

Continuous |
height, weight, LDL |
The change in the dependent variable per unit change in the independent variable. |
The change in the dependent variable per unit change in the independent variable after controlling for the confounding effects of the covariates in the model. |

Categorical (also known as "discrete") |
sex (2 subgroups, men (sex =1) and women (sex = 2) where one is designated as the reference group (men, in this example). |
The difference in the dependent variable for one value of categorical variable (e.g., the difference between women and the reference group, men). |
The difference in the dependent variable for one value of categorical variable (e.g., between women and the reference group men), after controlling for the confounding effects of the covariates in the model. |

SUDAAN ((*proc regress)*, SAS Survey (*proc survey reg*)*, and *
Stata (*svy:regress*)
procedures produce b coefficients,
standard errors for these coefficients, confidence intervals, a t-statistic for
the null hypothesis (i.e., b =0), a
p-value for the t-statistic (i.e., the probability of obtaining a value greater
than or equal to the value for the t statistic).

In addition to the t-test, SUDAAN produces other test statistics with their corresponding p-values. These include the WALD F, Satterthwaite adjusted F, and Satterthwaite adjusted chi square statistics. SAS Survey procedures only produces the Wald F test with their corresponding p-values.

At the present time, the NHANES Analytic Guidelines do not make a recommendation about which statistic is the " best." Users are encouraged to frequently check the NHANES website for updated analytic guidelines. In the meantime, it is a good practice to examine all three statistics and the corresponding p-values for consistency. Users also are encouraged to compare the nominal degrees of freedom (i.e. the number of PSUs minus the number of strata containing observations) to the adjusted Satterthwaite degrees of freedom. Nominal degrees of freedom that are much larger than the adjusted Satterthwaite degrees of freedom may indicate model instability.

Generally speaking, the Satterthwaite adjusted F is the most conservative of the three statistics (i.e., it rejects the null hypothesis less often than do the other two statistics).