Variance vs Trend in Sales | Dataford Interview Questions

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Business Context

NorthPeak Retail is reviewing weekly revenue for one product line after a pricing update. The VP asks whether recent movement should be explained as normal week-to-week variability or as a real upward trend.

Problem Statement

Use the data below to explain the difference between variance analysis and trend analysis, then quantify both on the same dataset. Variance analysis should compare actual revenue to budget week by week. Trend analysis should evaluate whether revenue is systematically increasing over time.

Given Data

Week	Budget Revenue ($000)	Actual Revenue ($000)
1	100	98
2	100	101
3	100	103
4	100	102
5	100	106
6	100	108
7	100	109
8	100	111

The analyst will use a significance level of 0.05 for the trend test.

Requirements

Compute the weekly variance from budget and the average variance across all 8 weeks.
Compute the sample variance and sample standard deviation of actual weekly revenue.
Fit a simple linear trend model with week number as the predictor and actual revenue as the response.
Test whether the slope is significantly greater than 0 at $\alpha = 0.05$ .
Explain, in plain language, how variance analysis and trend analysis answer different business questions.

Assumptions

Weekly observations are ordered in time and measured consistently.
A linear trend is a reasonable first-pass model over 8 weeks.
Residuals from the linear model are approximately independent and normally distributed for inference.