Dean made a statistical estimation of the cost-output relationship for a shoe store. The data for the firm is given in the following table. x 4.5 7 9 10 15 20 33 50 y 3 3.3 3.4 3.5 4.5 5.5 7.5 12 Here x is the output in thousands of pairs of shoes, and y is the cost in thousands of dollars. A. Determine the best-fitting line (using least squares). S1(x) = r2 = 0.9852 B. Determine the best-fitting quadratic (using the least squares) and the square of the correlation coefficient. S2(x) =
Added by Laura P.
Step 1
x_mean = (4.5 + 7 + 9 + 10 + 15 + 20 + 33 + 50) / 8 = 18.625 y_mean = (3 + 3.3 + 3.4 + 3.5 + 4.5 + 5.5 + 7.5 + 12) / 8 = 5.3375 Show more…
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The cost of manufacturing a lot of a certain product depends on the lot size, as shown below: Lot size, x | Cost, hundreds of dollars, y 1 | 2 5 | 9 10 | 16 25 | 35 50 | 65 100 | 120 250 | 275 500 | 495 a) Find the least squared estimators Sxx, Sxy and Syy b) Find the y-intercept, a, and slope, b c) Write the equation for the best fit line d) Using the best fit line, determine the cost estimate for a lot size of 1200 e) Determine the correlation coefficient, r, and comment on the relationship between cost and lot size.
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The following table contains pricedemand and total cost data for the production of regular sleeping bags, where $p$ is the wholesale price (in dollars) of a sleeping bag for an annual demand of $x$ sleeping bags and $C$ is the total cost (in dollars) of producing $x$ sleeping bags: $$ \begin{array}{clc} x & p & C \\ 2,300 & 98 & 145,000 \\ 3,300 & 84 & 170,000 \\ 4,500 & 67 & 190,000 \\ 5,200 & 51 & 210,000 \end{array} $$ (A) Find a quadratic regression equation for the pricedemand data, using $x$ as the independent variable. (B) Find a linear regression equation for the cost data, using $x$ as the independent variable. (C) What is the maximum profit? What is the wholesale price per regular sleeping bag that should be charged to realize the maximum profit? Round answers to the nearest dollar.
Graphing and Optimization
Optimization
Accountants for the HiTech Shoe Company have determined that the quadratic relation P=-2x^2+24x-54 models the company's profi for the next quarter. In this relation, P represents the profit (in 100 000 s) and x represents the number of pairs of shoes sold (in 100 000 s).Determine the number of pairs of shoes that the company must sell to maximize its profit. How much would the maximum profit be?
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