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# Regression Project: Data The table below contains the price, demand, and total cost data for the...

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.

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