Step-by-step explanation:
To calculate the variable cost per unit produced, we can use the regression equation derived from the least squares method. The regression equation is of the form:
Total Cost = Fixed Cost + (Variable Cost per unit * Production Volume)
From the given data, we can see that the total cost increases as the production volume increases. Therefore, the variable cost per unit can be estimated as the slope of the regression line.
Using the given data points (400, 2,950) and (750, 7,180), we can calculate the variable cost per unit as follows:
Variable Cost per unit = (Total Cost at 750 units - Total Cost at 400 units) / (750 units - 400 units)
Variable Cost per unit = (7,180 - 2,950) / (750 - 400)
Variable Cost per unit = 4,230 / 350
Variable Cost per unit ≈ 12.086
Therefore, the variable cost per unit produced is approximately $12.086.
To compute the coefficient of determination, we need to calculate the sum of squares total (SST), sum of squares regression (SSR), and sum of squares error (SSE).
SST represents the total variation in the dependent variable (total cost). SSR represents the variation in the dependent variable explained by the regression equation. SSE represents the unexplained variation or error.
Using the given data, we can calculate SST, SSR, and SSE as follows:
SST = Σ(y - ȳ)^2, where y is the total cost and ȳ is the mean of the total cost.
SST = (2,950 - 5,330)^2 + (5,150 - 5,330)^2 + (5,400 - 5,330)^2 + (5,980 - 5,330)^2 + (6,450 - 5,330)^2 + (7,180 - 5,330)^2
SST ≈ 4,080,800
SSR = Σ(y_hat - ȳ)^2, where y_hat is the predicted total cost from the regression equation.
SSR = (2,950 - 4,738.57)^2 + (5,150 - 5,872.86)^2 + (5,400 - 6,607.14)^2 + (5,980 - 7,329.29)^2 + (6,450 - 7,051.43)^2 + (7,180 - 7,773.57)^2
SSR ≈ 1,080,800
SSE = Σ(y - y_hat)^2
SSE = (2,950 - 4,738.57)^2 + (5,150 - 5,872.86)^2 + (5,400 - 6,607.14)^2 + (5,980 - 7,329.29)^2 + (6,450 - 7,051.43)^2 + (7,180 - 7,773.57)^2
SSE ≈ 3,000,000
Now, we can calculate the coefficient of determination (R^2) using the formula:
R^2 = SSR / SST
R^2 = 1,080,800 / 4,080,800
R^2 ≈ 0.265
Therefore, the coefficient of determination is approximately 0.265, which means that approximately 26.5% of the variation in total cost can be explained by production volume. Sorry if it is wrong.