Question

Consider the following data on the quantity of production and its cost (in dollars) for a particular customized component, for each of 10 weeks.

                                             NumberProduced                              Cost

                                                     16                                             207.17

                                                       6                                               90.93

                                                     18                                             227.22

                                                     10                                             153.61

                                                     13                                             155.97

                                                       3                                               68.24

                                                       9                                             112.00

                                                     16                                             185.77

                                                     20                                             260.48

                                                       5                                               80.62

a.   Find the usual statistical measure for the strength of the association between cost and number produced. Please give both the name and numeric value for your answer.

Name:

Numeric Value:

b.   Find, to the penny, the estimated cost of producing one additional component (this is the “variable cost” or the “variable cost of production”).

Variable Cost:

c.   How well has this variable cost (from part b) been estimated? Please answer by providing a 95% confidence interval for the true variable cost of this production process.

Confidence Interval:

d.   Estimate, to the penny, the cost associated with producing 12 units in a week, assuming the same process from which the data were obtained.

Cost to produce 12 units:

Answer 1

a) To test the measure of association between cost and number produced, pearson correlation should be used.

It can be calculated using excel .

Following are the steps:

Step 1: put the data into the spreadsheet

Step 2: Go to data --> data analysis --> correlation

Step 3: Select the data and get the output

a.

Name: Pearsons Correlation

Numerical measure = 0.9839

b. To estimate the cost of producing one additional component, we need to perform the regression analysis and get the regression equation.

Step 1: go to data --> data analysis --> regression

Step 2: select the data ( choose cost as y variable, number produced as x variable) and get the output

The regression equation: y = 26.227 + 11.03x

Hence, the cost producing one additional component is $ 11.03

c) The 95% percent confidence interval is given in the regression output

The confidence interval is (9.4014 , 12.662)

So, the variable cost is part b is well estimated as $ 11.03 comes between the confidence limits

d) The cost to produce 12 units

Cost (y) = 26.227 + 11.03 * 12= $ 158.587