a. Suppose Y; = B1x; + €;, i = 1,...,n. In this equation x is non-random, ß1 is a parameter (unknownbut not random), e ~not adjust it to be unbiased.N (0, o), and €1, ..., En are independent. Find the MLE of o². Is it unbiased? Ifb. Refer to question (a). Let S2 be the unbiased estimator of o?. Use all the details (distribution theory,(n-1)S?independence, moment generating functions) to find the distribution ofc. Use the result from question (b) and also the distribution of 6Bị to construct a t ratio. What are thedegrees of freedom of this t ratio? Note: Bị is the MLE of B1.- a prediction interval for Y can be constructed for a given new value x0. Note: Thed. Explain how a 1prediction of Y is given by Yo = B1x0. Also, assume that Yo is not one of the Y1,..., Yn values.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If the dependent variable Y correlates with the independent variable X, this suggest that X has a causal impact on Y. Select one: True False
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For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.4, y = 6.0, r=-0.233, P-value = 0.104, and ŷ= 7.88 -0.292x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.01 significance level. The best predicted value of y when x = 4 is (Round to one decimal place as needed.)

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Suppose Y; = B1x; + €;, i = 1, ...,n. In this equation x is non-random, ß1 is a parameter (unknown but not random), e ~ N(0, 0), and €1,..., En are independent. Find the MLE of o². Is it unbiased? If not adjust it to be unbiased.