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## How, if at all, does caffeine intake affect hormone levels in women

(1 pt) 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(E2), and how that may depend on daily caffeine intake (in mg per day). Suppose the scatter plot of the logarithm of the estradiol level(Y)against daily caffeine intake(X)appeared as below:A linear regression model fitted to the above scatter plot isY=3.3369+0.000591XJennifer 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 141.94 mg/day and had a recorded log(E2)level of 3.4. Compute the residual for this observation, to two decimal places.Part b)Suppose the ANOVA table for the regression is as below:SourceCaffeineErrorTotalDoFSS6.165.64711.807MS(i)(ii)FProvide the missing entries, to two decimal places.(i):(ii):Part c)Based on the above information, we wish to test the null hypothesis that log(E2)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 logE2level does not depend linearly on daily caffeine intake? A. Reject B. Not reject

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