Regression Analysis Project. Regression Report: Price, Cost, Revenue, and Profit

Regression Report: Price, Cost, Revenue, and Profit
Student’s Name
Institutional Affiliation
Regression Report: Price, Cost, Revenue, and Profit
Price
Usually, a regression function for price is P(x) = m x + b. For this report, the regression function for price and demand as the dependent and independent variable respectively was Price(x) = - 0.92121(x) + 154.86667. X was the number of widgets in terms of demand for annual widgets.
On a scatterplot, the data fitted using the regression line was plotted, as shown below.
Agreeably, the regression line (red) modeled the data well because most of the data points fall along with it. The regression equation was used to estimate price at P (0), P (35), and P (105). The prices, $153.94546, $122.62432, and $58.13962 were obtained for 0, 35 and 105 widgets. The value of x that would make P (x) = 0 would be 168.11223282422 widgets.
Cost
A cost regression function was also of the form was C = m x + b. Through the provided data, the total cost was the dependent variable, while the number of widgets was the independent variable. The regression function for total cost would be Cost = 49.99636x + 4.71985. On a scatterplot fitted with the regression line, the plot was displayed as below.
The regression line (green) modeled the data well because all the data points fell along the line. The regression equation was also used to estimate C (0), C (35), and C (105). The cost values were $4.71985, $1,754.59245, and $5,254.33765 for 0, 35, and 105 widgets. Using the regression equation, the fixed cost of the widget was $49.99636, while the variable cost was $4.71985.
Revenue
Assuming that the annual widget sales matched the annual widget demand, a model for revenue using the model for price was constructed. Equating R (x) to x ∗ p (x), the model constructed using P (x) was R(x) = x*P (x). After equating the formula for price of x widgets, R(x) was R(x) = x* (-0.92121(x) + 154.86667). Computing further generated the formula for R(x) as R(x) = -0.92121x2 + 154.86667x. The number of widgets to be sold to yield positive revenue would be 154.86667/0.92121 = 168.1122328. The number of widgets that should be sold to maximize revenue would be -b/2a, which is equal to -154.86667/2(-0.92121). The result after this computation was 84.056116. The maximum revenue would be -0.92121(84.056116)2 + 154.86667(84. 056116) = $6,508.74542.
Profit
Recall that profit can be computed in terms of revenue and cost.  Assume that the annual widget sales match the annual widget demand and annual widget production.  A model for profit using the models for revenue and cost that you found in the Revenue and Cost sections would be
P(x) = R (x) - C(x) where R(x) = -0.92121x2 + 154.86667x and C(x) = 49.99636x + 4.7...