The dataset Amanda has compiled includes:

The response variable 'Subscribe', which is binary, indicating whether a customer chose to subscribe $(1)$ or not $(0)$ following the campaign.

The continuous predictor variable 'Discount', representing the percentage reduction in price offered to the customer.

The continuous predictor variable 'Age', denoting the age of the customer.

The categorical predictor variable 'Sex', indicating the gender of the customer.

The logistic regression model will enable Amanda to predict the probability of subscription for potential customers based on the given predictors. Additionally, by examining the model's coefficients, she will be able to infer the strength and direction of the impact that each predictor has on the likelihood of a customer subscribing.

This analysis is not only expected to validate the effectiveness of the current marketing initiative but also to serve as a foundational model for future campaigns. By integrating the results of this analysis with the company's broader marketing strategy, Amanda aims to drive higher conversion rates, tailor the customer experience more closely to individual preferences, and ultimately, increase the firm's market share in the subscription space.