Quiz2-key

Quiz2-key - Re-arrange each function as follows b 2 x = ˆ...

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University of California, Davis ARE 106 - Winter 2011 Quiz 2 Name: Student Number: 1. The population regression function and the sample regression function are plotted in the graph below. The seventh observation from the data that generated the sample regression function, ( x 7 ,y 7 ), is also plotted on the graph. (a) Label ˆ y 7 , e 7 , ˆ e 7 , β 1 , and b 1 . (2 points each) (b) Re-arrange the population regression function and the sample regression function to solve for β 2 x and b 2 x . Brieﬂy show your work. Then label β 2 x 7 and b 2 x 7 on the graph. (Hint: you should be labelling a distance along the y-axis.) (4 points)
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Unformatted text preview: Re-arrange each function as follows: b 2 x = ˆ y-b 1 and β 2 x = E ( y | x )-β 1 . Note that E ( y | x 7 ) is a point on the population regression function line labelled above. (c) In this case, which is greater in absolute value: β 2 x 7 or b 2 x 7 ? (Hint: you can answer this without an answer for part (b).) (1 point) Because the slope of the sample regression function is greater than the population regression function, b 2 x 7 > β 2 x 7 . You can also see this by looking at the distances labelled on the graph above....
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