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Homework100B4

# Homework100B4 - be height and y i be weight for i = 1 10 63...

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STAT 100B HW 4 Due Friday 5pm Problem 1: For the simplest regression model y i = βx i + ± i , i = 1 ,...,n , derive the least squares estimate of β . Problem 2: For the simple regression y i = β 0 + β 1 x i + ± i , i = 1 ,...,n , derive the least squares estimates of β 0 and β 1 . Show that the least squares problem for the simple regression can be transformed into the least squares problem for the simplest regression. Problem 3: The following is a data set where the ﬁrst column records the heights (in the unit of cm) of 10 people randomly sampled from the population, and the second column records the weights (in the unit of kg) of the same people. Let x i
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Unformatted text preview: be height, and y i be weight, for i = 1 ,..., 10. 170 76 165 63 186 83 142 39 176 62 183 81 181 82 179 82 171 85 180 77 (1) Fit the simplest regression y i = βx i + ± i by estimating β by least squares. (2) Fit the simple regression y i = β + β 1 x i + ± i by estimating β and β 1 by least squares. (3) Using the learned simple regression, predict the weight of a person whose height is 175. (4) Draw (with your hands, not computers or calculators) the scatter plot and the ﬁtted regres-sion lines of the simplest regression and simple regression. 1...
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