A small business tracks how advertising spending relates to weekly sales.
$\left(B\right)$ Predict what the business would make in weekly sales if they spent \$400 in advertising.

• A. 10,200
• B. 10,250
• C. 8,235
• D. 9,749

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the problem. We want to predict the weekly sales when the advertising spending is \$400. This involves finding the relationship between advertising spending and sales from the given data.
2. Step 2: Plot or analyze the data to see if there is a linear relationship between advertising spending (independent variable) and sales (dependent variable). If the relationship appears linear, we can use linear regression to model it.
3. Step 3: Calculate the linear regression equation of the form \(\text{Sales} = m \times \text{Advertising} + b\), where \(m\) is the slope and \(b\) is the intercept. Use the formulas for slope and intercept:
4. \[m = \frac{n \sum (x_i y_i) - \sum x_i \sum y_i}{n \sum x_i^2 - (\sum x_i)^2}\]
5. \[b = \frac{\sum y_i - m \sum x_i}{n}\]
6. where \(x_i\) are advertising values, \(y_i\) are sales values, and \(n\) is the number of data points.
7. Step 4: Once you have the regression equation, substitute \(x = 400\) (advertising spending) into the equation to predict the corresponding sales value.
8. Step 5: Interpret the predicted sales value as the estimated weekly sales when the business spends \$400 on advertising.