To solve this regression problem, we will compute the regression coefficients $b_1$ (slope) and $b_0$ (intercept) using the least-squares method. Let's break it into steps:

Step 1: Formulas to Compute $b_1$ and $b_0$

The formulas for regression coefficients are: $b_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$ $b_0 = \bar{y} - b_1 \bar{x}$ where:

• $x_i$: Production Volume (units)
• $y_i$: Total Cost ($)
• $\bar{x}$: Mean of production volumes
• $\bar{y}$: Mean of total costs

Step 2: Calculate Averages

First, compute $\bar{x}$ and $\bar{y}$: $\bar{x} = \frac{\sum x_i}{n}, \quad \bar{y} = \frac{\sum y_i}{n}$

Step 3: Calculate Summations

Compute:

• $\sum x_i y_i$
• $\sum x_i^2$
• $\sum x_i$ and $\sum y_i$

Step 4: Solve

Plug in the values to calculate $b_1$, $b_0$, and the regression equation: $\hat{y} = b_0 + b_1 x$

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