Multiple Choice
A small business tracks how advertising spending relates to weekly sales.
Plot Advertising Spending (x) vs Sales (y) & find the regression line & correlation coefficient.
12. Regression
Prediction Intervals - Excel
Multiple Choice
A small business tracks how advertising spending relates to weekly sales.
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
Verified step by step guidance1
Step 1: Understand the problem. We want to predict the weekly sales when the advertising spending is \$400. This involves finding a relationship between advertising spending and sales.
Step 2: Plot or analyze the data to see if there is a linear relationship between advertising spending and sales. Since the data shows pairs of advertising and sales values, we can use linear regression to model this relationship.
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. To do this, compute the means of advertising and sales, the covariance between advertising and sales, and the variance of advertising.
Step 4: Use the formulas for slope and intercept:
\(slope\ m = \frac{\sum (Advertising_i - \bar{Advertising})(Sales_i - \bar{Sales})}{\sum (Advertising_i - \bar{Advertising})^2}\)
\(intercept\ b = \bar{Sales} - m \times \bar{Advertising}\)
Step 5: Substitute \(Advertising = 400\) into the regression equation \(Sales = m \times 400 + b\) to predict the sales for \$400 in advertising spending.
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