Calculate R2 for this regression model. Predict the response when a patient takes 5 table spoons per day.
Question 1
(Do it by hand and show all your steps. You may use R for double-checking, if you want) A medical study was designed to study the efficacy of a certain medication and its dose. In this study, X represents the dose, the number of table spoons of medication administrated per day; and Y represents the response, a self-reposted improvement score.
Patient A B C D E F X112233 Y 0 6 6 12 6 12
Fitting the linear regression model in R produced the following output. > reg = lm(Y ∼ X)
> reg
>anova(reg)
Analysis of Variance Table:
Response: Y
X Residuals
Coefficients: (Intercept) X
13
Df SumSq MeanSq Fvalue Pr(>F) 1 36 36.0 2.1818 0.2137 4 66 16.5
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(a) Calculate R2 for this regression model.
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(b) Predict the response when a patient takes 5 table spoons per day.
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(c) For the lack of fit test, state the null and the alternative hypotheses; calculate the extra sum of squares and the F-statistic.
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(d) (Stat-627 only) While solving part (c), at some point, you treated dose X as a categorical variable. Keeping X categorical, estimate the prediction mean square error by the LOOCV.
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(e) It was noticed that patients A,C and E took a generic, whereas patients B,D and F took the brand-name medicine. Based on the scatterplot, can you tell if the type of medicine has a non-zero interaction with the dose?
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