# sol2 - PSTAT 120C Assignment#2 Solutions 1(a Unemployment...

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PSTAT 120C: Assignment #2 Solutions April 24, 2006 1. (a) Unemployment rate is the independent variable, short term interest rate is the dependent random variable. (b) Snowfall is the independent random variable, yield is the dependent. (c) Net weight is the independent variable, mileage is the dependent variable. (d) Height of the towers is the independent variable, density of particles is the dependent variable. (e) Annual income of donors is the independent variable, amount of donation is the dependent variable. 2. Exercise 11.15 from the book (a) ˆ β 1 = S xy S xx = . 475 ˆ β 0 = ¯ y - ˆ β ¯ x = 10 . 6 - . 475(1 . 6) = 3 . 000 (b) The least squares line is y = 3 + 4 . 75 x (c) We calculate S yy - ˆ β 1 S xy = 112 . 4 - . 475(152) = 40 . 2 and s 2 = SSE n - 2 = 40 . 2 8 = 5 . 025 3. The independent variable is the average daily temperature. The dependent variable is the mean number of species. ˆ β 1 = s y s x r = 45 . 22 3 . 36 0 . 1465 = 1 . 97 ˆ β 0 = ¯ y - ˆ β 1 ¯ x = 65 . 73 - 1 . 97 * 2 . 59 = 60 . 63 An estimate of σ is s y n - 1 n - 2 (1 - r 2 ) = 45 . 22 10 9 (1 - 0 . 1465 2 ) = 47 . 15 4. The likelihood in this case where Y i is a normal with mean β 0 + β 1 x

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