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25. An important application of regression in manufacturing is the estimation of cost of production. Based...

25. An important application of regression in manufacturing is the estimation of cost of production. Based on DATA from Ajax Widgets relating cost (Y) to volume (X), what is the cost of producing 600 widgets?

Production Volume (units)

Total Cost $

400

3430

450

4080

550

4878

600

4884

700

5913

750

6402

425

4273

475

4362

575

5089

625

5446

725

6017

775

6591

Solutions

Expert Solution

Solution:

Given: cost (Y) and Production volume (X)

We have to find the cost of producing 600 widgets by using given data.

Thus we need to find regression equation to predict Y = Cost from X= Production volume.

where

Thus we need to make following table:

X : Production Volume (units) Y : Total Cost $ X^2 XY
400 3430 160000 1372000
450 4080 202500 1836000
550 4878 302500 2682900
600 4884 360000 2930400
700 5913 490000 4139100
750 6402 562500 4801500
425 4273 180625 1816025
475 4362 225625 2071950
575 5089 330625 2926175
625 5446 390625 3403750
725 6017 525625 4362325
775 6591 600625 5108025

Thus

Thus

and

Thus

Thus regression equation is:

Thus the cost of producing 600 widgets is:

orchestra answered 10 months ago
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