How, if at all, does caffeine intake affect hormone levels in women? Lucero et al. (2001) report a study involving a sample of 498 women from the general population aged between 36 and 45. The women each completed a questionnaire, including items on caffeine intake, and provided a blood sample collected during the early phase of the menstrual cycle. We focus here on the level of estradiol $\left( E_{2}\right)$, and how that may depend on daily caffeine intake (in mg per day). Suppose the scatter plot of the logarithm of the estradiol level $\left( Y\right)$ against daily caffeine intake $\left( X\right)$ appeared as below:



A linear regression model fitted to the above scatter plot is



Jennifer Lucero, Bernard L. Harlow, Robert L. Barbieri, Patrick Sluss, Daniel W. Cramer (2001): Early follicular phase hormone levels in relation to patterns of alcohol, tobacco, and coffee use. Fertility and Sterility 76, Issue 4, 723--729.

Part a)
Suppose one of the subjects reported a daily caffeine intake of mg/day and had a recorded log$\left(E_{2}\right)$ level of . Compute the residual for this observation, to two decimal places.


Part b)
Suppose the ANOVA table for the regression is as below:



Provide the missing entries, to two decimal places.
$\text{(i)}$: $\text{(ii)}$:

Part c)
Based on the above information, we wish to test the null hypothesis that log$\left( E_{2}\right)$ level does not depend linearly on daily caffeine intake. Provide the test statistic that would appear in the ANOVA table, to two decimal places.


Part d)
If testing at the 1% significance level, would you reject or not reject the null hypothesis that log $E_{2}$ level does not depend linearly on daily caffeine intake?

A. Reject
B. Not reject