IB Business Management HLTopic 6 — The Business Management ToolkitPapers 1, 2 & 3HL only~10 min read
Using Simple Linear Regression
Plot two things against each other, see whether they move together, then draw a straight line through the middle and use it to predict. That is the whole tool. The hard part is not the drawing, it is knowing when the prediction is worth trusting.
📘 What you need to know
A scatter graph plots two variables to see whether a relationship exists.
Positive correlation: both rise together. Negative: one rises as the other falls. None: no pattern.
The line of best fit (regression line) runs through the middle of the points, with roughly as many above as below.
Points close to the line = a strong correlation. Points scattered far from it = a weak one.
Extrapolation means extending the line past the data to predict. It assumes the past pattern continues.
Correlation is not causation. Two things moving together does not prove one caused the other.
The three patterns
The third panel matters as much as the first two. Sometimes the honest finding is that the two things are simply unrelated.
Drawing and using the line
Roughly as many points sit above the line as below it. The line does not have to touch any of them.
Reading the line
Two features of the line carry all the information:
The gradient tells you how much the second variable changes when the first goes up by one. In the graph above, sales rise by roughly 6.6 units for every extra $1,000 spent.
The intercept is where the line crosses the vertical axis: what you would expect with zero spending. Here that is about 13 units.
Using the line to forecast
predicted sales = 13 + (6.6 × advertising spend in $000)
WORKED EXAMPLE
Bright Batch plans to spend $8,000 on advertising next month. Use the line of best fit to forecast sales, and comment on how reliable your answer is. [4 marks]
Step 1: put the value into the line13 + (6.6 × 8) = 13 + 52.8Forecast sales: about 66 unitsStep 2: comment on reliabilityThe seven points sit close to the line, so the correlation is strong and the forecast is reasonable [1]. But $8,000 is beyond the data, which only ran to $7,000, so this is extrapolation and assumes the pattern keeps going [1]. In reality the effect of extra advertising usually flattens off once most likely customers have already seen the message [1].“strong correlation, but extrapolated” is exactly the balance examiners want
Correlation is not causation
This is the point that separates a good answer from an average one. Two variables can move together for three quite different reasons:
Explanation
What is going on
Example
Real cause
One variable genuinely drives the other
More advertising leads more people to visit the shop
A third factor
Something else drives both at the same time
Summer raises both ice cream sales and sun-cream sales
Coincidence
No connection at all; the data just happens to line up
Two unrelated figures both rising over five years
Before you accept a relationship, ask whether anything else could explain it. A bakery that advertises heavily every December will find a beautiful correlation between advertising and sales — but the real cause is Christmas.
Outliers. If more than one point sits well above the line, shift the line up a little. If more than one sits well below, shift it down. A single freak point should not move it at all.
How useful is it?
Strength
Weakness
Turns messy data into a clear visual pattern
Assumes the relationship is a straight line, which it often is not
Allows quick forecasting from a small data set
Extrapolation beyond the data can be badly wrong
Shows the strength of a relationship, not just its direction
Correlation never proves cause
Helps set budgets: what does one more dollar of spend buy?
Only handles two variables at a time
Easy to explain to non-specialists
Sensitive to outliers and to small samples
💡 Exam tips
Name the correlation precisely: strong positive, weak negative, or none.
Draw the line with a ruler, through the middle, with similar numbers of points either side.
Show the reading on the graph with dashed lines if you are asked to predict from it.
Always say whether you are interpolating (inside the data) or extrapolating (outside it).
Mention sample size. Seven months is thin evidence for a five-year plan.
Finish with the causation point. It is the highest-value sentence on this topic.
⚠ Common mix-ups
Joining the dots instead of drawing one straight line.
Assuming correlation proves cause. It never does on its own.
Extrapolating far beyond the data and treating the result as certain.
Letting one outlier drag the line away from everything else.
Confusing a strong correlation with a steep one. Strength is about closeness to the line, not gradient.
Putting the variables on the wrong axes. The thing you control goes on the horizontal axis.
Up next: Applying SWOT and STEEPLE to a Real Business — that is the toolkit complete. Now learn how to use the tools together on a case study under exam conditions.
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