Business Context

Streamly, a subscription video app, increased paid acquisition spend in several markets and wants to estimate how much weekly signups changed after controlling for seasonality and pricing. The goal is to use regression for product growth analysis rather than relying on a simple before/after comparison.

Problem Statement

You are given the output of a linear regression where weekly new signups are modeled as a function of paid marketing spend, average subscription price, and a holiday-week indicator.

Given Data

The fitted model is:

$\widehat{\text{signups}} = \beta_0 + \beta_1 \cdot \text{ad\_spend} + \beta_2 \cdot \text{price} + \beta_3 \cdot \text{holiday}$

where ad spend is measured in $1,000s, price in USD, and holiday is 1 for holiday weeks and 0 otherwise.

Additional information:

Requirements

1. Interpret the ad spend coefficient in business terms.
2. Test whether ad spend is significantly associated with signup growth at $\alpha = 0.05$.
3. Compute a 95% confidence interval for the ad spend coefficient.
4. Estimate the incremental weekly signups from increasing ad spend from 120 to 150.
5. Explain whether this regression supports a causal claim about growth.

Assumptions

• Use a two-sided t-test for coefficients.
• Degrees of freedom are $n-k-1$.
• Assume standard linear regression conditions hold unless discussed otherwise.