Exercise A .97 on page 189 , we introduce a study about mating activity of
water striders. The dataset is available as WaterStriders and includes the
variables FemalesHiding, which gives the proportion of time the female water
striders were in hiding, and MatingActivity, which is a measure of mean mating
activity with higher numbers meaning more mating. The study included 10 groups
of water striders. (The study also included an examination of the effect of
hyper-aggressive males and concludes that if a male wants mating success, he
should not hang out with hyper-aggressive males.) Computer output for a model
to predict mating activity based on the proportion of time females are in
hiding is shown below, and a scatterplot of the data with the least squares
line is shown in Figure 9.12 .
The regression equation is MatingActivity \(=0.480-0.323\) FemalesHiding
\(\begin{array}{lrrrr}\text { Predictor } & \text { Coef } & \text { SE Coef }
& \text { T } & \text { P } \\ \text { Constant } & 0.48014 & 0.04213 & 11.40
& 0.000 \\ \text { FemalesHiding } & -0.3232 & 0.1260 & -2.56 &
0.033\end{array}\)
\(\begin{array}{lll}S=0.101312 & \text { R-Sq }=45.1 \% & \text { R-Sq(adj)
}=38.3 \%\end{array}\)
Analysis of Variance \(\begin{array}{lrrrrr}\text { Source } & \text { DF } &
\text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression
} & 1 & 0.06749 & 0.06749 & 6.58 & 0.033 \\ \text { Residual Error } & 8 &
0.08211 & 0.01026 & & \\ \text { Total } & 9 & 0.14960 & & & \end{array}\)
(a) While it is hard to tell with only \(n=10\) data points, determine whether
we should have any serious concerns about the conditions for fitting a linear
model to these data.
(b) Write down the equation of the least squares line and use it to predict
the mating activity of water striders in a group in which females spend \(50
\%\) of the time in hiding (FemalesHiding = 0.50)
(c) Give the hypotheses, t-statistic, p-value, and conclusion of the t-test of
the slope to determine whether time in hiding is an effective predictor of
mating activity.
(d) Give the hypotheses, F-statistic, p-value, and conclusion of the ANOVA
test to determine
whether the regression model is effective at predicting mating activity.
(e) How do the two p-values from parts (c) and (d) compare?
(f) Interpret \(R^{2}\) for this model.
