Question

Regression Project: Data

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

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: Price

1. Use the given data to find a regression line that best fits the price-demand data for price p in dollars as a function of the demand x widgets. Here, price is the dependent variable, and demand is the independent variable. Find the regression function for price, and write it as p ( x ) = m x + b.

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

   • Make a title for the plot "Price of Widgets".

   • Label your axes. Label the horizontal axis "Annual widget demand", and label the vertical axis "Price per widget ($)".

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

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

5. What value of x would make p ( x ) = 0? Give the real-world interpretation of the result of the computation in complete sentences. Be sure to include units.

Answer 1