Prism reports the parameter estimates in two ways.

•The parameter estimates' effects on the log odds (remember that log odds = β0 + β1 * X1 + β2 * X2 + ...).

•An interpretation of the multiplicative change on the log odds in the form of odds ratios

Additional information on P values calculated for these parameter estimates is provided elsewhere.

Parameter interpretations

Interpreting parameter estimates for logistic regression is more complicated than for linear regression. The reason is that we have transformed Y to model the log odds. The beta coefficient estimates listed under "Parameter estimates" in the output have the following interpretation:

If we are talking about β2, we can say that for a 1 unit increase in X2, the log odds of Y increases by β2, when all the other X values are held constant.

Since most people don’t intuitively think in terms of log odds, Prism also offers interpretation based on odds ratios.

Standard errors and confidence intervals

Similar to many other analyses (such as multiple linear regression), the only way to know the actual, true value of a given parameter is to collect information on the entire population. For example, if you wanted to know average human weight, you could (hypothetically), measure the weight of every single human and calculate the average. However, since you can’t actually collect data from every person, you collect a sample. The average that you collect from that sample will have some error due to random variability in the subjects that you selected. For multiple logistic regression, Prism reports two values that provide an idea as to the amount of error in the estimates of the provided parameter coefficients: standard error and profile likelihood confidence intervals.

The standard error of a coefficient can be difficult to interpret, but in simple terms, it provides an idea for how precise the parameter estimate is.

Another way to look at this concept of precision is with confidence intervals, which provide you with some idea of how sure you can be of the provided coefficient estimate. The general concept is that if the experiment were repeated a huge number of times and confidence intervals constructed for the parameter coefficient each time, 95% of these intervals (for a 95% confidence interval) would contain the true parameter coefficient for the population. Note that some software reports symmetric confidence intervals calculated using the standard error described above. Prism actually calculates more accurate (but also slightly more complicated) profile likelihood confidence intervals. These can be (usually are) asymmetric around the parameter value.