Question

Maps Course Home For this Final Exam, each snort answer submission that does not have a nanawriten response wir receive a mark of ZERO. Question 70 4 pts For the data below: 1. (1 Point) - Find the regression equation for predicting Y from X. 2.13 Points - Calculate the predicted for each X value, find each residual, square each residual and add the squared values to obtain SS residual

Answer 1

L X 4 3 7 6 10 Y 2 4 6 3 5 x 16 9 49 36 100 y2 4 16 36 9 25 XY 8 12 42 18 50 Y pred 3.33 3.00 4.33 4.00 5.33 (Y -Y pred)^2 1.78 1.00 2.78 1.00 L L 0.11 Total 30 20 2 10 90 130 6.67 beta = alpha= 0.33 2
$\\ Regression\ equation\ of\ Y\ on\ X\ is:\\ Y = \alpha + \beta X,\ where\\ \\ \beta = {n\sum(xy) - \sum x \sum y \over n\sum x^2 - (\sum x)^2}\\ and\\ \alpha = {\sum y - \beta \sum x \over n}$

$\\ We\ have\\ \sum X = 30,\ \sum Y = 20,\ \sum X^2 = 210,\ \sum Y^2 = 90,\ \sum XY = 130\\ \\ \beta = {5*130 - 30*20 \over 5*210 - (30)^2} = 0.33\\ and\\ \alpha = {20 - 0.33* 30 \over 5} = 2\\ Hence,\ the\ regression\ equation\ of\ Y\ on\ X\ is:\\ Y = 2 + 0.33 X.$

$\\ SS_{residual} = 6.67\ \ \ \ \ \ \ \ \left \{ as\ obtained\ in\ above\ table. \right \}$