What does the Wald statistic test in regression models?

What does the Wald statistic test in regression models?

• A. A test statistic to test whether a coefficient is significantly different from zero.
• B. A test statistic used to assess model fit.
• C. A test statistic to determine if a predictor's coefficient is significantly different from zero.
• D. A test statistic for residual normality.

Answer: (C)

Wald tests are used to evaluate hypotheses about regression coefficients. Specifically, they test whether a predictor’s coefficient is zero, meaning the predictor has no effect on the outcome. The statistic combines the estimated coefficient with its standard error; for a single coefficient, it equals (β̂ / SE(β̂))^2 and follows a chi-square distribution with 1 degree of freedom in large samples (the square of the usual t-statistic). This is how you determine if a predictor is significantly associated with the outcome. It’s not used to assess overall model fit or residual normality, which rely on different tests; the Wald framework can also extend to testing multiple coefficients together.

Wald tests are used to evaluate hypotheses about regression coefficients. Specifically, they test whether a predictor’s coefficient is zero, meaning the predictor has no effect on the outcome. The statistic combines the estimated coefficient with its standard error; for a single coefficient, it equals (β̂ / SE(β̂))^2 and follows a chi-square distribution with 1 degree of freedom in large samples (the square of the usual t-statistic). This is how you determine if a predictor is significantly associated with the outcome. It’s not used to assess overall model fit or residual normality, which rely on different tests; the Wald framework can also extend to testing multiple coefficients together.