Business Context

StreamCart’s growth team launched a new executive dashboard showing average order value (AOV) by marketing channel. The raw chart suggested paid social outperformed email, but channel mix also differed by device, and mobile users typically spend less. An analyst used regression adjustment to improve the visualization so leadership could compare channels on a like-for-like basis.

Problem Statement

Use the regression output below to determine whether the apparent AOV difference between channels remains statistically significant after controlling for device type, and quantify the adjusted effect that should be shown in the visualization.

Given Data

The analyst fit the linear model:

$AOV_i = \beta_0 + \beta_1 \cdot PaidSocial_i + \beta_2 \cdot Mobile_i + \varepsilon_i$

where Email and Desktop are the reference categories.

Additional model information:

Requirements

1. State the null and alternative hypotheses for the Paid Social effect.
2. Compute the 95% confidence interval for the adjusted Paid Social coefficient.
3. Determine whether the adjusted effect is statistically significant at $\alpha = 0.05$.
4. Compare the raw difference with the regression-adjusted difference.
5. Explain how this regression improves the visualization shown to executives.

Assumptions

• The linear model is correctly specified for this simple adjustment.
• Observations are independent.
• Residuals are approximately mean-zero with constant variance.
• Use a large-sample normal approximation for inference.