Question

2. This week, we studied the test score Y versus number of hours, X, spent on test preparation, of a student in a French class of 10 students with the collected results shown below Number of hours studied Test score 31 10 14 73 37 12 60 91 21 84 17 (a) Use linear normal regression analysis method or the least-squares approximation method to predict the average test score of a student who studied 12 hours for the test (b) Do you find any inconsistency of your result in (a) with the data shown in the table? Give your explanation. 3. (Continued from Problem 2) With linear normal regression analysis, do the following. (a) Construct a 95% confidence interval for ß where Y|x ~ N(o +fa, σ2) (b) Find the critical region for the hypothesis testing Ho:B-3.5, Hi : B3.5, with 0.05 as the level of significance, and use the data provided to make your decision 5. (An extension of ideas of linear normal regression analysis) Let X,Y be random variables such that for any given X-x the variable Y follows a normal distribution with mean which is allowed to be quadratic in z, and variance σ2. In this problem, you are given an opportunity to extend the ideas of linear regression to tackle a more general situation. You are to follow the steps below to present your own formalism (a) Let (,, (n) be observed data readings of the pair (X,Y). Construct the likelihood function from the data. b) Obtain the equations satisfied by α β, γ σ such that the likelihood function in a) is maximized. (c) Use (b) to predict the average test score of a student who studied 12 hours for the test using the data of Problem 2 and compare your finding here with that in Part (a) of Problem 2. Does anything alert you?

Answer 1

nen hat 2) 2 223 782. 88477 ct 4752. 690834 326 2. 842 Cs Scanned with CamScanner

pedicted vaue CS Scanned with CamScanner