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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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