Question

Production Volume (units)	Total Cost ($)
400	4000
450	5000
550	5400
600	5900
700	6400
750	7000

Production Target	Est. Cost ($)
500

• Compute b₁ and b₀ (to 1 decimal).

  b₁

  b₀

  Complete the estimated regression equation (to 1 decimal).

  y = ... + x

• According to this model, what is the change in cost (in dollars) for every unit produced (to 1 decimal)?

• Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.

  r² =

  What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?

  ... %

• The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?

  $ ...

Answer 1

	Production X	Total Cost Y	X * Y
	400	4000	1600000	160000	16000000
	450	5000	2250000	202500	25000000
	550	5400	2970000	302500	29160000
	600	5900	3540000	360000	34810000
	700	6400	4480000	490000	40960000
	750	7000	5250000	562500	49000000
Total	3450	33700	20090000	2077500	1.95E+08

Equation of regression line is


b = 7.6

a =( 33700 - ( 7.6 * 3450 ) ) / 6
a = 1246.7
Equation of regression line becomes

b0 = 1246.7

b1 = 7.6

r = 0.979

Coefficient of Determination

Explained variation = 0.959* 100 = 95.9%
Unexplained variation = 1 - 0.959* 100 = 4.1%

When X = 500
= 1246.667 + 7.6 X
= 1246.667 + 7.6 * 500
= 5047