The cost of preparing meals in a school canteen is linearly related to the number ofmeals prepared, as shown in the table. The equation of the least squares regression line which relates them is shown below: cost = 81.5 + 2.10 × number of meals Use the equation to predict the cost of producing 48 meals. (Write your answer in the format $xxx.xx)

Question

The cost of preparing meals in a school canteen is linearly related to the number ofmeals prepared, as shown in the table. The equation of the least squares regression line which relates them is shown below: cost = 81.5 + 2.10 × number of meals Use the equation to predict the cost of producing 48 meals. (Write your answer in the format $xxx.xx)

BlackTom AI · Accepted Answer

We are given a linear relationship between cost and number of meals described by the regression line: cost = 81.5 + 2.10 × (number of meals).

Step 1: Identify the input value. Here, the number of meals is 48.

Step 2: Substitute 48 into the equation for the variable part. Compute 2.10 × 48.

Step 3: Multiply: 2.10 × 48 = 100.8.

Step 4: Add the intercept. Add 81.5 to 100.8 to get the total cost: 81.5 + 100.8 = 182.3.

Step 5: Since the problem asks for the answer in the format $xxx.xx, express 182.3 as $182.30.

Common mistakes to watch for: forgetting the intercept 81.5, miscomputing 2.10 × 48 (e.g., using 2.1 × 48 without aligning decimal places), or failing to format the final amount with two decimals. The procedure above follows the regression model exactly and ensures two-decimal formatting.

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