reghw6.htm

# reghw6.htm - Regression We shall be looking at regression...

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Regression We shall be looking at regression solely as a descriptive statistic: what is the line which lies 'closest' to a given set of points. 'Closest' shall be defined as minimizing the sum of the squared y (vertical) distance of the points from the regression line (which is more fully called the least squares regression line). We shall not derive the formula, merely present it and then use it. Data is given as a set of points in the plane, i.e., as ordered pairs of x and y values. Formulæ Example Formulæ x-bar = *sum* x(i)/n This is just the mean of the x values. y-bar = *sum* y(i)/n This is just the mean of the y values. SS_xx = *sum* (x(i)-(x-bar))^2 This is sometimes written as SS_x (_ denotes a subscript following). SS_yy = *sum* (y(i)-(y-bar))^2 This is sometimes written as SS_y. SS_xy = *sum* (x(i)-(x-bar))(y(i)-(y-bar)) b_1 = (SS_xy)/(SS_xx) (_ denotes a subscript following) b_0 = (y-bar) - (b_1) × (x-bar) The least squares regression lilne is: y-hat (lowercase y with a caret circumflex) = (b_0) + (b_1) × x Example What is the least squares regression line for the data set {(1,1), (2,3), (4,6), (5,6)}?

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