Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 41 / 2 / ii / Solution

The Wald test of $H_0:\beta =0$ useswith an approximate standard normal distribution under the null. Its two-sided p-value is $0.403$, and the approximate $95\%$ Wald confidence interval isThere is no convincing evidence of a covariate effect, and the slope is very imprecisely estimated. The model can fit acceptably while its slope is statistically indistinguishable from zero. In the Poisson regression, a unit covariate increase multiplies the mean by $e^{\beta }$; exponentiating the two interval limits shows how poorly this multiplier is determined on the stated scale. One might compare with an intercept-only model using a likelihood-ratio test, but its numerical deviance difference is not supplied. Failure to reject does not establish no effect.