c. Consider the simple regression model without intercept y; = 1 ; + i= 1, . . ., n. Assume that 19 . . . ; n are independent and i N(0, o ) and that T 1, . .., , are not random. Construct a prediction interval for Y, for a given new To . d. Refer to question (c). Find a confidence interval for the expected value of Yo for a given new T.. e. Refer to question (c). Develop the likelihood ratio test for testing H. :3 , = 0 against H. :3 = 0 and show that it follows the F distribution