Regression Analysis
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Kyle Ashcraft, CPA · 2019 CPA Exam Scores · 95 FAR · 98 BEC · 91 REG · 90 AUD
Sometimes you need to understand how two things move together — like a restaurant's sales on game days versus non-game days. That's what regression analysis is for.
What is regression analysis?
Regression analysis looks at the relationship between two variables: an independent variable and a dependent variable. The dependent variable is determined by the independent variable — not the other way around.
If you're calculating total production costs, the number of units produced is the independent variable (X), and total cost is the dependent variable (Y), since cost depends on how many units you make.
- Y — the dependent variable you're solving for (total costs)
- X — the independent variable (units produced)
- M — the slope, or how much Y changes per one-unit increase in X (the variable cost per unit)
- B — the Y-intercept, or fixed costs, which don't change regardless of X
Study tip: Memorize Y = MX + B cold — nearly every regression question on the exam is built around plugging numbers into this formula.
Worked example
Company A produced 1,000 widgets this month. Fixed costs are $2,000, and the variable cost per unit is $3. What were total costs?
Y is total costs (what we're solving for), X is 1,000 units, M is $3, and B is $2,000:
What is the coefficient of determination?
The coefficient of determination, written R², measures what proportion of the change in Y is explained by X. It ranges from 0 to 1: zero means none of the change in Y is explained by X; one means all of it is.
Study tip: R² is also called "goodness of fit" — the closer to 1, the better X explains Y. If you're choosing between two possible formulas on the exam, pick the one with the higher R².
What is the coefficient of correlation?
The coefficient of correlation, written R (not R²), describes how related two variables are — without implying one causes the other. It ranges from −1 to +1, and there's no formula to calculate it; it's a measure of association.
Study tip: R ranges from −1 to +1. A coffee shop that sells 10% more coffee every time it rains 10% more has a perfect positive correlation (R = +1). If it instead sold 10% less coffee every time it rained 10% more, that's a perfect negative correlation (R = −1).
What is the high-low method?
When you're not given fixed costs or variable cost per unit directly, the high-low method estimates them from the difference between your highest- and lowest-activity periods.
Study tip: Take the difference between the highest-activity month and the lowest-activity month — both in units and in cost — then divide.
Say the past three months looked like this:
| Month | Units Sold | Total Cost |
|---|---|---|
| June | 700 | $6,000 |
| July | 750 | $6,200 |
| August | 800 | $6,500 |
August is the high month, June is the low month. The difference is 100 units (800 − 700) and $500 in cost ($6,500 − $6,000):
Using June to solve for fixed costs:
Regression analysis, R², R, and the high-low method all describe the relationship between two variables from a different angle. Y = MX + B gives you the cost equation itself; R² and R tell you how much to trust it; the high-low method lets you build that equation from raw data when you aren't handed it directly.
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Kyle Ashcraft, CPA scored 90 or above on every section of the CPA exam in 2019, including a 98 on BEC. He is the founder and sole instructor of Maxwell CPA Review, a complete CPA review course covering all six sections, where he creates every lecture, textbook and study outline himself.
