Regression Project: Data

The table below contains the price, demand, and totalcost data for the production of x widgets. Here p is the price (indollars) of a widget for an annual demand of x widgets, and C isthe annual total cost (in dollars) of producing x widgets peryear.

Demand x (widgets)	Price p ($/widget)	Total Cost C ($)
10	141	609
20	133	1103
30	126	1618
40	128	2109
50	113	2603
60	97	3111
70	90	3619
80	82	4103
90	79	4601
100	53	5114

Regression Project: Cost

1. Use the given data to find a regression line C = m x + bthat best fits the total cost data for total annual cost C as afunction of the annual number of widgets produced x. Here, totalcost is the dependent variable, and number of widgets is theindependent variable. Find the regression function for cost, andwrite it as C ( x ) = m x + b.

2. Use the data to make a scatter plot. Include yourregression line on the same plot. Adjust the max/min to display thedata in a reasonable way. On the plot, be sure to

   • Make a title for the plot \"Annual Total Cost ofProducing Widgets\".

   • Label your axes. Label the horizontal axis \"Annualwidget production\", and label the vertical axis \"Annual total cost($)\".

3. Does it look like the regression line models the datawell? Why or why not?

4. Use the regression function you found to estimate C ( 0), C ( 35 ), and C ( 105 ). Give the real-world interpretation ofthe result of each computation in complete sentences. Be sure toinclude units.

5. Using your regression function for cost, what is thefixed cost? What is the variable cost? Give the real-worldinterpretation of the result of each computation in completesentences. Be sure to include units.