Exercise 7.4 introduced a study about Wolbachia and reproductive success in a wasp host. The following table shows the model coefficients for a model predicting the number of eggs laid over a lifetime from the predictor variables wolbachia density and tibia length. A higher number of eggs laid over a lifetime is indicative of greater reproductive success. The model has \(R^{2}=0.314\) and degrees of freedom 34. The \(F\)-statistic is 7.782 , with \(p\)-value 0.0016 .

(a) Write the model equation.

(b) Interpret the slope coefficient of wolbachia.

(c) Assess the evidence for whether Wolbachia is beneficial for its host in nature, based on these data.

(d) Compute and interpret a \(95 \%\) confidence interval for the population slope of wolbachia.

(e) Interpret the significance of the \(F\)-statistic.

Data From Exercise 7.4

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Estimate Std. Error t value Pr(>|t|) (Intercept) -17.88 28.63 -0.62 0.537 wolbachia 4.28 1.25 3.42 0.002 tibia 0.272 0.16 1.69 0.010