Inference on parameters

We set variables appropriately for the logistic regression model

$\displaystyle \mathrm{logit}($Probability for "Yes"$\displaystyle ) = \beta_0 + \beta_1 x_{1j} + \beta_2 x_{2j} + \cdots + \beta_k x_{kj},
\quad j=1,\ldots,n,

starting from the response of Yes and No. Then set the columns for predictors from X1 up to X9. Data is obtained for all the different groups or conditions, summarized in n of these combinations.

The result of fitting the logistic regression is obtained in the table below.

For each of the parameters from the intercept $ \beta_0$ to the coefficients $ \beta_1,\ldots,\beta_k$, the summary result shows:

  1. The estimate $ \hat{\beta}_i$ of "log odds ratio" is given for each parameter.
  2. The 95% confidence interval (L.Bound, U.Bound) is calculated for $ \beta_i$.
  3. The null hypothesis $ H_0: \beta_i = 0$ is constructed, and the p.value is obtained.
  4. The estimate $ e^{\hat{\beta}_i}$ of odds ratio (OR) is obtained.