Quiz_6_Solutions1 - Quiz 6 Solutions Course: Stat 231 Term:...

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Unformatted text preview: Quiz 6 Solutions Course: Stat 231 Term: Spring 2010 Instructor: Dr. Jock MacKay Prepared by: Murshid Kuttihassan 1. (1 mark)The parameter α represents C: the average value of the response variate when the explanatory variate has value ¯ x To see this, first set x i = ¯ x in the regression equation to obtain Y i = α + β (¯ x- ¯ x ) + R i = α + R i Now take expectation on both sides to obtain E [ Y i ] = E [ α ] + E [ R i ] = α + 0 = α Hence α is the average of Y i when x i = ¯ x . 2 (1 mark)The larger the value of σ B: the greater the variation when the same unit is measured repeatedly The value of Y depends on both x and R i . When x is held constant the variation in Y is normally distributed with standard deviation σ . For higher values of σ the variation will be higher. 3 (1 mark)If μ ( x ) = α + β ( x- ¯ x ) represents the average response variate for a unit with explanatory variate value x , then the maximum likelihood estimate of μ (5) is (to two decimal places) Answer: 4 . 04 ± . 01 1 We first estimate ˆ α and ˆ β ....
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This note was uploaded on 03/20/2011 for the course STATISTICS 231 taught by Professor Mckay during the Spring '10 term at Waterloo.

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Quiz_6_Solutions1 - Quiz 6 Solutions Course: Stat 231 Term:...

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