Homework Soursedevelop the estimated regression equation for these data Pro
develop the estimated regression equation for these data. Production Volume (units) Total Cost ($) 400 4000 450 5000 550 5400 600 5900 700 6400 750 7000
Solution
Mean of X = X / n = 575
Mean of Y = Y / n = 5616.6667
(Xi - Mean)^2 = 93750
(Yi - Mean)^2 = 5648333.33
(Xi-Mean)*(Yi-Mean) = 712500
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 712500 / 93750 = 7.6
bo = Y / n - b1 * X / n
bo = 5616.6667 - 7.6*575 = 1246.6667
Y = bo + b1 X
Y\'=1246.6667+7.6*X
Mean of X = X / n = 575
Mean of Y = Y / n = 5616.6667
(Xi - Mean)^2 = 93750
(Yi - Mean)^2 = 5648333.33
(Xi-Mean)*(Yi-Mean) = 712500
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 712500 / 93750 = 7.6
bo = Y / n - b1 * X / n
bo = 5616.6667 - 7.6*575 = 1246.6667
Y = bo + b1 X
Y\'=1246.6667+7.6*X
Mean of X = X / n = 575
Mean of Y = Y / n = 5616.6667
(Xi - Mean)^2 = 93750
(Yi - Mean)^2 = 5648333.33
(Xi-Mean)*(Yi-Mean) = 712500
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 712500 / 93750 = 7.6
bo = Y / n - b1 * X / n
bo = 5616.6667 - 7.6*575 = 1246.6667
Y = bo + b1 X
Y\'=1246.6667+7.6*X
Mean of X = X / n = 575
Mean of Y = Y / n = 5616.6667
(Xi - Mean)^2 = 93750
(Yi - Mean)^2 = 5648333.33
(Xi-Mean)*(Yi-Mean) = 712500
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 712500 / 93750 = 7.6
bo = Y / n - b1 * X / n
bo = 5616.6667 - 7.6*575 = 1246.6667
Y = bo + b1 X
Y\'=1246.6667+7.6*X
Mean of X = X / n = 575
Mean of Y = Y / n = 5616.6667
(Xi - Mean)^2 = 93750
(Yi - Mean)^2 = 5648333.33
(Xi-Mean)*(Yi-Mean) = 712500
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 712500 / 93750 = 7.6
bo = Y / n - b1 * X / n
bo = 5616.6667 - 7.6*575 = 1246.6667
Y = bo + b1 X
Y\'=1246.6667+7.6*X
Mean of X = X / n = 575
Mean of Y = Y / n = 5616.6667
(Xi - Mean)^2 = 93750
(Yi - Mean)^2 = 5648333.33
(Xi-Mean)*(Yi-Mean) = 712500
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 712500 / 93750 = 7.6
bo = Y / n - b1 * X / n
bo = 5616.6667 - 7.6*575 = 1246.6667
Y = bo + b1 X
Y\'=1246.6667+7.6*X
| Line of Regression Y on X i.e Y = bo + b1 X | ||||
| Xi | Yi | (Xi - Mean)^2 | (Yi - Mean)^2 | (Xi-Mean)*(Yi-Mean) |
| 400 | 4000 | 30625 | 2613611.2 | 282916.67 |
| 450 | 5000 | 15625 | 380277.82 | 77083.34 |
| 550 | 5400 | 625 | 46944.459 | 5416.67 |
| 600 | 5900 | 625 | 80277.759 | 7083.33 |
| 700 | 6400 | 15625 | 613611.06 | 97916.66 |
| 750 | 7000 | 30625 | 1913611 | 242083.33 |
