Interpretation Of Regression R

Interpretation Of Regression R

Your company provides a variety of delivery services. Management wants to know the volume of a particular delivery that would generate $11,000 per month in operating profits before taxes. The company charges $22 per delivery. The controller’s office has estimated overhead costs at $9,900 per month for fixed costs and $12 per delivery for variable costs. You believe that the company should use regression analysis.

Your analysis shows the results to be: Monthly overhead = $26,501 + $10.70 per (number of deliveries). Your estimate was based on the following data: Month Overhead Costs Number of Deliveries 1 $159,630. Please analyze the data and your results, explaining your reasoning for supporting or rejecting your cost equation, showing all calculations. Additionally, write a report to inform management about the correct delivery volume required to generate $11,000 in monthly operating profits before taxes.

Paper For Above instruction

In analyzing the delivery service's overhead costs and estimating the necessary delivery volume to achieve a target profit, it is crucial to scrutinize the regression results and compare them to the company's original cost estimates. The regression equation obtained is: Monthly overhead = $26,501 + $10.70 per delivery, which indicates a fixed cost component of $26,501 and a variable cost of $10.70 per delivery. On the other hand, the company's prior estimates specify fixed costs at $9,900 and variable costs at $12 per delivery. This discrepancy warrants in-depth analysis to understand its implications and reliability.

Analysis of Data and Results

The primary approach involves comparing the regression output with the company's estimations. The regression suggests a higher fixed cost ($26,501 vs. $9,900) and a slightly lower variable cost per delivery ($10.70 vs. $12). To validate the regression model's accuracy, statistical measures such as the R-squared value, standard error, and p-values should be examined, though they are not provided here. Nonetheless, understanding the potential causes of mismatch is vital.

One possible reason for the higher fixed costs indicated by the regression could be that the model captures all overhead costs, including some variable components misclassified or additional fixed expenses not accounted for initially. Alternatively, the regression could be influenced by outlier months or limited data points, leading to overestimation of fixed costs or underestimation of variable costs.

To evaluate the credibility of the regression equation, residual analysis and the coefficient of determination must be considered. If residuals are randomly dispersed around zero and the R-squared value is high, the model is reliable. If not, the estimate may be biased or less accurate.

Furthermore, the regression’s slope of $10.70 signifies the marginal overhead cost per delivery, which aligns well with the company's variable estimate of $12, suggesting reasonable accuracy in variable cost estimation. The notable difference in fixed costs warrants consideration: the actual fixed costs are likely closer to the original estimate ($9,900) given that fixed costs are typically more stable over time.

Therefore, supporting the regression model for variable cost estimation makes sense, but the fixed cost component appears overestimated—possibly inflated by temporary or non-recurring costs in the sample period. These factors suggest a cautious interpretation: using the regression for variable costs is appropriate while adjusting fixed costs closer to the original estimate for planning purposes.

Calculations and Determination of Delivery Volume for $11,000 Profit

The company charges $22 per delivery. To generate a profit of $11,000, the total revenue must cover both costs and profit:

Total revenue = Delivery volume * $22 per delivery.

Using the regression model, total overhead costs (estimated) for a given delivery volume (D) are:

Overhead = $26,501 + $10.70 * D.

Variable cost per delivery (from regression) = $10.70, consistent with findings, and fixed costs = $26,501.

Assuming the original estimate of fixed costs ($9,900) is more reliable, we adjust fixed costs accordingly for calculations.

Step 1: Calculate contribution margin per delivery

Selling price per delivery = $22.

Variable cost per delivery = $10.70.

Contribution margin per delivery = $22 - $10.70 = $11.30.

Step 2: Calculate total fixed costs and total costs at breakeven

Using the regression fixed costs ($26,501), fixed costs are higher, so total costs for D deliveries:

Total Costs = Fixed costs + Variable costs = $26,501 + $10.70 * D.

Step 3: Formulate the profit equation

Total revenue = $22 * D.

Total costs = $26,501 + $10.70 * D.

Profit = Revenue - Costs = $22D - ($26,501 + $10.70D).

Set profit goal at $11,000:

$22D - ($26,501 + $10.70D) = $11,000.

Step 4: Solve for D (delivery volume)

$22D - $10.70D = $11,000 + $26,501.

($22 - $10.70)D = $37,501.

$11.30 D = $37,501.

D = $37,501 / $11.30 ≈ 3,320 deliveries.

Conclusion

To generate an operating profit of $11,000 per month before taxes, the company needs to deliver approximately 3,320 units monthly. This calculation reflects the regression-derived fixed overhead component, which is somewhat higher than the company's original estimate. The divergence indicates potential overhead costs that are not directly attributable to deliveries or are non-recurring. Management should consider using the more conservative fixed cost estimate ($9,900) from their initial data for budgeting purposes, which would lower the needed delivery volume slightly.

Adjusting fixed costs to $9,900, the calculations are:

Total Costs = $9,900 + $10.70 * D.

Then, the delivery volume D is calculated as:

$11.30 D = $11,000 + $9,900 = $20,900.

D = $20,900 / $11.30 ≈ 1,849 deliveries.

Therefore, depending on the fixed costs assumption, the required delivery volume ranges from approximately 1,849 to 3,320 units to achieve the profitability goal.

In conclusion, the regression analysis provides valuable insights into overhead costs, but managerial judgment and fixed cost stability must guide the final decision. Employing the regression results for variable costs but relying on known fixed costs ensures a balanced and accurate delivery volume forecast.

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