An operation research analyst investing the relationship between production lot

Question

An operation research analyst investing the relationship between production lot size (x) and the average production cost per unit (y). A study of recent operations provides the following data:

x 100 120 140 160 180 200 220 240 260 280 300

y $9.73 9.61 8.15 6.98 5.87 4.98 5.09 4.79 4.02 4.46 3.82

The analyst suspects that a piecewise linear regression model should be fit to these data. Estimate the parameters in such a model assuming that the slope of the line changes at x = 200 units. Do the data support the use of this model?

Explanation / Answer

By using excel we can solve this question.

First, enter data into excel.

Least square Regression line is = a + bx

Here a is intercept and b is the slope.

We have to find values of a and b.

For finding value of 'a' use excel command =INTERCEPT(select y values , select x values)

We get a = 12.291

For finding value of b use excel command =SLOPE(select y values , select x values)

We get b = -0.031

So Least square Regression line is = 12.291 – 0.031*x

a) For x = 200

   = 12.291 – 0.031*200

      = 12.291 – 6.2

     = 6.091

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