Homework100B5

Homework100B5 - STAT 100B HW 5 Due Friday 5pm Problem 1:...

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STAT 100B HW 5 Due Friday 5pm Problem 1: For the simplest regression model y i = βx i + ϵ i , i = 1 , ..., n , suppose we want to estimate β using penalized least squares by minimizing f ( β ) = n i =1 ( y i - βx i ) 2 + λ | β | , where λ is a given positive constant. Find ˆ β . How does ˆ β change with λ ? Problem 2: For the regression model y i = β 1 x i, 1 + β 2 x i, 2 + ... + β p x i,p + ϵ i , i = 1 , ..., n , derive the least squares estimates of β 1 , ..., β p using vector and matrix notation. Problem 3 optional: In the following data set, the four columns are, respectively, mother’s height, father’s height, gender of the child (1: male, 0: female), and child’s height (in adulthood,
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