Skip to content

Management Accounting · Analytical techniques in budgeting and forecasting

Linear Regression and the High-Low Method Explained

Updated 11 October 2026 · Fact-checked

Both methods split a mixed cost into a fixed part (a) and a variable cost per unit (b) so that y = a + bx. The high-low method uses only the highest and lowest activity points. Least squares regression uses all data points and gives a best-fit line. Solve b first, then a.

Understand Linear Regression and High-Low Method

Many costs are semi-variable. They have a fixed element that stays the same and a variable element that rises with activity. Your bank sees only the total cost each period. You need to split it into the two parts so you can forecast and budget.

We write the cost line as y = a + bx. Here y is total cost, a is the fixed cost, b is the variable cost per unit of activity, and x is the activity level (units, hours and so on).

The high-low method picks the period with the highest activity and the period with the lowest activity. The extra cost between them must come from the extra activity, because fixed cost does not change. So b = change in cost ÷ change in activity. Then you put b back into either point to find a. It is quick, but it ignores all other data, so one unusual point can distort the answer.

Least squares regression fits the line that minimises the sum of squared gaps between the actual points and the line. It uses every observation, so it is usually more reliable. In the exam you are normally given the formula for b, or the summary totals, and asked to calculate a and b.

Both methods assume a linear relationship and are only reliable for forecasting inside the range of the data (interpolation). Forecasting outside the range (extrapolation) is less reliable.

Key formulas to remember

Linear cost equation
y = a + bx
a = fixed cost, b = variable cost per unit, x = activity level.
High-low variable cost
b = (cost at highest activity − cost at lowest activity) ÷ (highest activity − lowest activity)
Choose the points by activity level, not by cost.
High-low fixed cost
a = total cost at either point − (b × activity at that point)
Using either point gives the same a.
Regression slope b
b = (nΣxy − ΣxΣy) ÷ (nΣx² − (Σx)²)
n is the number of data pairs. Calculate b before a.
Regression intercept a
a = (Σy ÷ n) − b × (Σx ÷ n)
This is mean of y minus b times mean of x.
Forecast
y = a + b × x
Substitute the planned activity level x.

How to solve Linear Regression and High-Low Method questions

Use this order for any high-low or regression question. Decide which method the question asks for first.

  1. 1Identify x (activity, the independent variable) and y (cost, the dependent variable).
  2. 2For high-low, pick the highest and lowest activity levels, not the highest and lowest costs.
  3. 3Calculate b: the change in cost divided by the change in activity.
  4. 4Calculate a by substituting b and one data point into y = a + bx.
  5. 5For regression, find n, Σx, Σy, Σxy and Σx² if they are not given, then apply the formula for b.
  6. 6Calculate a from the means: a = ȳ − b x̄.
  7. 7Write the equation y = a + bx and substitute the forecast activity level.
  8. 8Check your answer is sensible: b should be positive for most cost lines and a should be a plausible fixed cost.

Quickest way: Fast route for objective test questions

When to use it: Use when the question gives summary totals or two clear activity points and asks for a single value.

  1. For high-low, subtract the two rows on your calculator: cost difference ÷ activity difference gives b.
  2. Store b in memory, then calculate a from the lower activity point.
  3. For regression with totals given, work out the numerator and denominator of b separately, then divide.
  4. Calculate a with the means, not with the totals, to avoid scale errors.
  5. Forecast last, and check the units (thousands of units or hours) match the question.

Common mistakes in Linear Regression and High-Low Method

  • Choosing the highest and lowest cost instead of the highest and lowest activity.

    The cost column is the one that stands out, so students scan it first.

    Fix: Look only at the activity column when picking the two points. Use the costs that go with those activity levels.

  • Calculating a before b in regression.

    The equation is written a + bx, so students assume a comes first.

    Fix: The formula for a needs b. Always work out b first.

  • Mixing up Σx² and (Σx)².

    The two look similar and give very different numbers.

    Fix: Σx² means square each x and then add. (Σx)² means add all x and then square the total.

  • Using the wrong units, such as thousands of units with costs in dollars.

    Data tables often state units in headings only.

    Fix: Read the headings and convert at the end. If x is in thousands, the forecast x must be in thousands too.

  • Forecasting far outside the data range and treating the answer as reliable.

    The equation will always produce a number, so it feels valid.

    Fix: State that extrapolation is less reliable. In the test, still calculate the figure the question asks for.

  • Assuming high-low is more accurate than regression because it is simpler.

    Students confuse ease of calculation with quality.

    Fix: Remember high-low uses just two points and can be distorted by outliers. Regression uses all points.

Worked examples

Example 1

A company records these maintenance costs. Month 1: 2,000 machine hours, $38,000. Month 2: 3,500 machine hours, $52,000. Month 3: 2,800 machine hours, $45,000. Month 4: 3,000 machine hours, $46,000. Using the high-low method, estimate the total cost for 3,200 machine hours.

Show the solution
  1. Highest activity is 3,500 hours at $52,000. Lowest is 2,000 hours at $38,000.
  2. Change in cost = 52,000 − 38,000 = $14,000.
  3. Change in activity = 3,500 − 2,000 = 1,500 hours.
  4. b = 14,000 ÷ 1,500 = $9.3333 per hour (keep as a fraction, 28 ÷ 3).
  5. a = 38,000 − (9.3333 × 2,000) = 38,000 − 18,666.67 = $19,333.33.
  6. Forecast for 3,200 hours = 19,333.33 + (9.3333 × 3,200) = 19,333.33 + 29,866.67 = $49,200.

Answer: Estimated total cost for 3,200 machine hours is $49,200.

Example 2

A regression of cost (y, in $) on output (x, in units) uses 5 observations with these totals: Σx = 50, Σy = 400, Σxy = 4,300, Σx² = 540. Calculate a and b, then forecast cost for 12 units.

Show the solution
  1. n = 5.
  2. b = (nΣxy − ΣxΣy) ÷ (nΣx² − (Σx)²).
  3. Numerator = (5 × 4,300) − (50 × 400) = 21,500 − 20,000 = 1,500.
  4. Denominator = (5 × 540) − (50)² = 2,700 − 2,500 = 200.
  5. b = 1,500 ÷ 200 = 7.5.
  6. Mean y = 400 ÷ 5 = 80. Mean x = 50 ÷ 5 = 10.
  7. a = 80 − (7.5 × 10) = 80 − 75 = 5.
  8. Equation: y = 5 + 7.5x.
  9. Forecast for x = 12: y = 5 + (7.5 × 12) = 5 + 90 = 95.

Answer: a = $5, b = $7.50 per unit, and the forecast cost for 12 units is $95.

Exam tips

  • Read the question for the method named. If it says high-low, do not use regression, and the other way round.
  • In multiple choice, wrong options are often built from common errors, such as using highest cost points or forgetting to square before adding. Do your own calculation before looking at the options.
  • For number entry, keep full calculator accuracy until the final step and round only as the question instructs.
  • Check the units of x and y in the data table before you substitute into the equation.
  • Be ready for short theory points: regression uses all data, high-low uses two points, and both assume a linear relationship.

Practice questions from Analytical techniques in budgeting and forecasting

Linear Regression and High-Low Method in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Linear Regression and High-Low Method: frequently asked questions

What is the difference between the high-low method and regression analysis?

The high-low method uses only the highest and lowest activity points to estimate the fixed and variable cost. Regression uses all observations and finds the best-fit line. Regression is generally more reliable, but takes more calculation.

How do I calculate a and b in least squares regression?

Calculate b first using b = (nΣxy − ΣxΣy) ÷ (nΣx² − (Σx)²). Then calculate a using a = mean of y − b × mean of x. Finally write the line as y = a + bx.

Does the high-low method use the highest and lowest costs?

No. It uses the highest and lowest activity levels, together with the costs recorded at those levels. The highest cost is often at the highest activity, but not always.

Will I be given the regression formula in the ACCA MA exam?

Do not rely on it. Learn the formulas for a and b so you can use them quickly. Practise with summary totals so the calculation is routine.