Business Context
BrightCart, a DTC e-commerce company, wants to understand whether page load time is a meaningful driver of landing-page conversion. An analyst aggregated 12 weekly observations and fit a simple linear regression with weekly conversion rate as the outcome and average page load time as the predictor.
Problem Statement
Use the regression output to quantify the relationship between load time and conversion, test whether the slope is statistically different from zero, and assess whether the result is strong enough to guide product decisions.
Given Data
The model is:
conversion_ratei=β0+β1⋅load_timei+εi
| Metric | Value |
|---|
| Number of weekly observations n | 12 |
| Mean load time xˉ | 2.85 seconds |
| Mean conversion rate yˉ | 0.0610 |
| Sxx=∑(xi−xˉ)2 | 2.420 |
| Estimated slope β^1 | -0.0085 |
| Estimated intercept β^0 | 0.0852 |
| Residual sum of squares SSE | 0.000198 |
| Significance level α | 0.05 |
Interpretation note: conversion rate is measured as a proportion, so a slope of −0.0085 means a 1-second increase in load time is associated with a 0.85 percentage point decrease in conversion.
Requirements
- State the null and alternative hypotheses for the slope.
- Compute the residual variance and the standard error of the slope.
- Calculate the t-statistic and two-sided p-value for β^1.
- Construct a 95% confidence interval for the slope.
- Interpret the coefficient in business terms.
- Explain what this regression can and cannot tell you about what drives conversion.
Assumptions
- Weekly observations are independent enough for a basic regression screen.
- Linearity between average load time and average conversion rate is a reasonable approximation.
- Residual variance is constant across weeks.
