Business Context
CareBridge, a telehealth platform, is reviewing weekly customer support call volume after a new onboarding flow launched. Operations wants to know whether recent changes reflect normal week-to-week variability or a real upward trend that requires staffing changes.
Problem Statement
Use the data below to distinguish variance analysis from trend analysis. Variance analysis compares each week's actual calls to the weekly forecast, while trend analysis evaluates whether call volume is systematically increasing over time.
Given Data
| Week | Forecasted Calls | Actual Calls |
|---|
| 1 | 1000 | 980 |
| 2 | 1020 | 1015 |
| 3 | 1010 | 1040 |
| 4 | 1030 | 1060 |
| 5 | 1025 | 1085 |
| 6 | 1040 | 1110 |
| 7 | 1035 | 1135 |
| 8 | 1050 | 1160 |
Assume a significance level of α=0.05.
Requirements
- Compute the weekly variance between actual and forecasted calls.
- Calculate the mean variance and identify whether actual performance is generally above or below forecast.
- Fit a simple linear trend model of actual calls versus week number.
- Test whether the slope is significantly greater than 0.
- Explain, in plain language, the difference between what variance analysis tells you and what trend analysis tells you.
- Recommend what CareBridge should do operationally based on the results.
Assumptions
- Weekly observations are ordered in time and measured consistently.
- A linear trend is a reasonable first approximation over this 8-week period.
- Forecasts were set before observing actual calls.
- Ignore holiday effects and other external shocks for this exercise.
