Computing the least squares regression line. A graduate student surveys undergra

Question

Computing the least squares regression line. A graduate student surveys undergraduates study habits on his university campus. He asks students in different years in college how many hours of course work they do for each class each week. A samples of four students provides the following date on year in college and hours of course work per class: You want to predict the hours of course work per class (y) from the year (x) using a least squares regression line y = b_0 + b_1 x. The sample mean x for year is ____, and the sample mean y for hours of course per class is ____. Use your calculated sample mean values to complete the following table. One formula for the slope of the regression line following table. Enter the values for the numerator and denominator, and then enter the value of b_1. b_1 = sigma (x_i - x)(Y_ i - y)/sigma (x_ i - x)^2 =

Explanation / Answer

b1 = (xi - xbar)(yi - ybar ) / (xi - xbar)2 = -5/ 5 = -1

Student I Year(xi) Hour (yi) xi - xbar yi - ybar (xi - xbar)(yi - ybar ) (xi - xbar)2 1 1 7 -1.5 2 -3 2.25 2 2 5 -0.5 0 0 0.25 3 3 4 0.5 -1 -0.5 0.25 4 4 4 1.5 -1 -1.5 2.25

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