这是一个的R统计作业作业案例分享
Instructions: Questions labeled with ‘(R)’ require use of R. Please provide appropriate
R commands and their output, along with sufficient explanation and interpretation of the
output to demonstrate your understanding. Such R output should be presented in an
integrated form together with your explanations; do not attach them as separate
sheets. All other questions should be completed without reference to any R commands or
output. Make sure you give enough explanation so your tutor can follow your reasoning if
you happen to make a mistake. Please also try to be as succinct as possible. Each assignment
will include marks for good presentation and for attempting all problems.
1. (R) Let X and Y be the scores in Probability (MAST20004) and Statistics (MAST20005),
respectively, for a student who took both of these two subjects. A sample of n = 15
students yielded the following data:

(a) Fit a simple linear regression model E(Y jX = x) = α + βx for these data. Find
point estimates of α and β. What are the standard errors of these estimates
(b) Give a 95% confidence interval for the score in Statistics with a score of 70 in
Probability.
(c) Give a 95% prediction interval for the score in Statistics with a score of 70 in
Probability. Compare the prediction interval to the confidence interval obtained
in (b).
(d) Use a t-test to test H0 : β = 0:8 against H1 : β 6= 0:8 at the α = 0:05 significance
level and state your conclusion.
(e) Give the ANOVA table for the regression model.
(f) Use the ANOVA table (F-test) to test H0 : β = 0 against H1 : β 6= 0 at the
α = 0:05 significance level and state your conclusion.
(g) Let ρ be the correlation coefficient between X and Y , find an approximate 90%
confidence interval for ρ.
2. Assume that the distribution of X is N(μ; 25). To test the null hypothesis H0 : μ = 10
against the alternative hypothesis H1 : μ < 10, let the critical region be defined by C = fxˉ : ˉ x ≤ 8g, where ˉ x is the sample mean of a random sample of size n = 25 from N(μ; 25). (a) Find the power function K(μ) for this test . Hint: power is a function of the true parameter value. (b) What is the significance level of the test (c) What are the values of K(8) and K(6) (d) (R) Sketch a graph of the power function. Hint: you may try μ from 4 to 12. (e) What conclusion do you draw from the following 25 observations of X 12.1 24.0 9.8 7.0 6.0 6.9 6.8 9.5 11.8 10.1 8.1 0.1 4.7 13.6 11.3 7.2 0.4 10.7 13.1 7.0 18.4 4.0 2.8 12.0 15.9 (f) What is the p-value of the test based on the observations in (e)