are106-quiz3-key

# are106-quiz3-key - by \$762 In the second model if height...

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University of California, Davis ARE 106 - Winter 2011 Quiz 3 Name: Student Number: 1. To derive the R 2 statistic, we decomposed the sum of squares about y i into three parts, giving a name and acronym for each. The formulas for these parts are given below. Identify each part and state which one must always be larger than the other two. (8 points) n X i =1 ( y i - ˆ y ) 2 SSE n X i =1 ( y i - ¯ y ) 2 SST. It is always greatest; recall SST = SSE + SSR n X i =1 y i - ¯ y ) 2 SSR 2. We are interested in the eﬀect of height, H i on earnings, E i . Our dataset contains E i , a person’s average annual income in dollars and H i , his or her height in inches. We estimate the regression model: (1) E i = β 1 + β 2 H i + e i We ﬁnd b 1 = 10 , 000, b 2 = 762. We convert height in inches, H i , to height in centimeters, H cm i by multiplying by a conversion factor. We estimate the model: (2) E i = β 1 + β 2 H cm i + e i We ﬁnd that b 1 = 10 , 000 and b 2 = 300. (a) Interpret the b 2 estimates for each model in words. (i.e. If (blank) increases by (blank), we estimate that (blank).) (3 points) In the ﬁrst model: if height increases by one inch, we expect that income increases

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Unformatted text preview: by \$762. In the second model: if height increases by one centimeter, we expect that income increases by \$300. (b) Which model (1 or 2) provides better goodness-of-ﬁt to the data? Why? (4 points) Both models ﬁt the data equally well. Scaling the data does not change the R 2 which measures the goodness of ﬁt. In other words, we can measure our variables in which ever units we prefer and the conclusions drawn from our regression model remain the same. University of California, Davis ARE 106 - Winter 2011 (c) How could you solve for the conversion factor between inches and centimeters? (2 bonus points) You could divide b inches 2 by b cm 2 to get the conversion factor. The conversion factor is the constant c in the algebraic representation of scaling the data presented in class....
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are106-quiz3-key - by \$762 In the second model if height...

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