Business Context
AdBoost, a digital marketing agency, seeks to understand the effectiveness of its advertising campaigns on sales performance. To quantify this impact, the company collected data over the last quarter on advertising spend and corresponding sales figures.
Given Data
| Week | Advertising Spend ($) | Sales ($) |
|---|
| 1 | 500 | 5,000 |
| 2 | 700 | 6,500 |
| 3 | 1,200 | 9,000 |
| 4 | 900 | 7,500 |
| 5 | 1,500 | 10,000 |
| 6 | 1,000 | 8,000 |
Task
Determine whether there is a statistically significant relationship between advertising spend and sales.
Requirements
- Formulate the null and alternative hypotheses.
- Fit a linear regression model to the data.
- Calculate the coefficient of determination (R²) to assess the model fit.
- Conduct a hypothesis test for the slope coefficient to determine its significance.
- Interpret the results in the context of AdBoost's advertising strategy.
Assumptions
- The relationship between advertising spend and sales is linear.
- The residuals of the regression model are normally distributed and homoscedastic.
