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443hw1w10

# 443hw1w10 - The weight of the bats in 30 consecutive days...

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Homework Assignment 1 STAT 443 Forecasting: Due Date: February 1, 2010 Drop Box: TBA 1) (10 points) Prove the following statement There exists a linear relationship between two random variables U and V, i.e. V = a+bU, if and only if the correlation coefficient ρ (U,V) has an absolute value of 1 2) (10 points)Show that, if U and V are random variables following a Normal distribution, the assumption of independence is equivalent to the assumption of uncorrelatedness. 3) (30 points) In order to manufacture bats for the game of professional cricket, each bat has to be of a specific weight. Every machine that produces cricket bats has a certain target value β 0 (representing the ideal weight) and that is aimed by calibrating the machine carefully.

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Unformatted text preview: The weight of the bats in 30 consecutive days is obtained and is given in the data set below. If the machine is calibrated correctly, and if the OLS assumptions hold, we would expect a constant mean model with the Yt’s fluctuating randomly around the target value β . The data set Y t ; t=1,2,…30 37, 27, 25, 32, 29, 30, 31, 33, 34, 38, 33, 31, 37, 41, 26, 32, 37, 31, 25, 35, 36, 39, 31, 32, 28, 34, 30, 27, 26, 38. (i) Find the OLS estimate for β , i.e β * , and a 95% confidence interval for β (ii) Find a 95% prediction interval for Y t , where t>30 (iii) Run a residual diagnostic test for the OLS assumptions, checking for heteroscedasticity, uncorrelatedness and normality...
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443hw1w10 - The weight of the bats in 30 consecutive days...

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