How much bread will the cafés want?: Lena's Bakery Ltd does not only sell over its three counters. Every night the Mill Lane bakehouse also bakes for cafés and hotels in town (wholesale), and in 2025 that brought in $240,000.
Marco has to plan 2026 and 2027: how much flour to order from Valley Grain, how many van runs, whether the ovens can cope. 4.3.1 showed why a forecast is worth having. This micro is how to make one from the figures Lena already has.
| Year | Wholesale sales ($000) | Rise on the year before ($000) |
|---|---|---|
| 2019 | 100 | none, the first year |
| 2020 | 120 | 20 |
| 2021 | 140 | 20 |
| 2022 | 165 | 25 |
| 2023 | 185 | 20 |
| 2024 | 215 | 30 |
| 2025 | 240 | 25 |
Read down the middle column and one thing stands out: the figure goes up every year, by $20,000 to $30,000. That general direction over time, ignoring the small ups and downs, is the trend. A set of figures recorded one after another over time (a time series) is where a trend is read from.
Turning the table into a line graph
One axis for time
Put the years 2019 to 2025 along one axis, evenly spaced. Label it: Year.
One axis for sales
Put sales on the other, from 0 to 300 in equal steps, and label it with the unit: Wholesale sales ($000). A label without its unit leaves the reader guessing.
Plot each year
One point per row of the table: 2019 at 100, 2020 at 120, and so on to 2025 at 240.
Join the points
Join each point to the next with a straight line. That makes it a line graph, and the trend shows as the way the line climbs.
A line graph is not yet a forecast: The joined-up line goes through every point, wobbles included, and it stops at 2025.
To look past 2025, Lena needs something different: one straight line that sums up all seven years at once.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
A line of best fit is one straight line, drawn with a ruler through the middle of the points, that sums up the trend. Some points sit a little above it and some a little below, and all of them close. It does not have to pass through any point, not even the first or the last one.
Lena's wholesale sales, read forward
Lay the ruler through the middle
The line that fits the seven points best starts at about 96 in 2019 and reaches about 237 in 2025. It passes just under 2019, 2020, 2024 and 2025, and just over 2021, 2022 and 2023.
Find the yearly rise
From 96 to 237 is a rise of about 141 over six years: about 23 ($23,000) a year on the line.
Extend the line
Carry the same straight line on past 2025, with the same ruler, into 2026 and 2027. Reading values off the line beyond the last real point is extrapolation.
Read off the forecast
2026: about 237 + 23 = 260, so $260,000. 2027: about 260 + 23 = 283, so $283,000.
What the forecast is saying: Extrapolation says: if the next two years go the way the last seven did, wholesale sales will be about $260,000 in 2026 and $283,000 in 2027.
Marco can now order flour and book van runs for about $283,000 of wholesale bread by 2027, not for the $240,000 he sold in 2025.
| Year | Actual wholesale sales ($000) | On the line of best fit ($000) |
|---|---|---|
| 2019 | 100 | 96 |
| 2021 | 140 | 143 |
| 2023 | 185 | 190 |
| 2025 | 240 | 237 |
| 2026 | not yet known | 260, the forecast |
| 2027 | not yet known | 283, the forecast |
Two ways to spoil the reading: Bending the line. Extrapolation carries the same straight line on. A line that curves up to meet the last point, or that is redrawn from 2025 alone, is no longer the line of best fit.
Joining the dots. Extending the last jump (2024 to 2025, up 25) instead of the line through all seven years gives 265 and 290: it lets one year speak for seven.
Practice with real exam questions
Answer exam-style questions and get AI feedback that shows you exactly what examiners want to see in a full-marks response.
A shop with no past: The fourth shop, on Station Road, has not opened yet. It has no sales to plot and no line to extend.
So Lena forecasts its sales from something she can measure today.
Valley Grain, the farmers' cooperative that mills Lena's flour, supplies eight bakeries in nearby towns. With their permission it shares two figures for each: how many people walk past the door in an hour at lunchtime (footfall), and the bakery's weekly bread sales. Lena stands outside the empty shop on Station Road with a clicker and counts 240 people an hour.
| Bakery | People passing per hour | Weekly bread sales ($) |
|---|---|---|
| A | 120 | 3,330 |
| B | 150 | 4,030 |
| C | 180 | 4,420 |
| D | 210 | 4,780 |
| E | 250 | 5,560 |
| F | 280 | 5,940 |
| G | 320 | 6,510 |
| H | 360 | 7,350 |
Independent variable
- The figure you know, or can measure now: people passing per hour
- It goes along the bottom (the horizontal axis)
- Lena counted it for Station Road: 240
Dependent variable
- The figure you want to forecast: weekly bread sales
- It depends on the other one, so it goes up the side (the vertical axis)
- For Station Road it is the unknown
Simple linear regression
- The straight line of best fit that links the dependent variable to the independent one
- Simple: one independent variable. Linear: a straight line
- Plotted as dots, not joined: a scatter diagram
The Station Road forecast
The scatter diagram
Plot the eight bakeries as eight dots: footfall along the bottom, weekly sales up the side. Do not join them; the order of the bakeries means nothing.
The regression line
A spreadsheet fits the line of best fit through the dots. In words: weekly bread sales = $1,500 + $16 for every person passing per hour.
Read off Station Road
$1,500 + $16 × 240 = $5,340 a week. On the graph: go up from 240 to the line, then across.
Turn it into loaves
At $3 a loaf, $5,340 is 1,780 loaves a week: about 254 a day over seven days. That is where Lena's target of 250 loaves a day for Station Road comes from.
Time can be the independent variable too: Lena's wholesale line was the same tool: the year was the independent variable and sales the dependent one.
Extend a line along time and it is a trend forecast. Read it at a footfall of 240 and it is a forecast for a shop that does not exist yet.
How much should Lena trust $5,340? That depends on how tightly the dots sit around the line. How closely two variables move together is their correlation, and a scatter diagram shows two things about it: its direction and its strength.
Positive correlation
- As one rises, the other rises: the dots climb from bottom left to top right
- Valley Grain's footfall and bread sales: more people passing, more bread sold
Negative correlation
- As one rises, the other falls: the dots slope down from top left to bottom right
- Valley Grain's loaf prices: the dearer bakeries tend to sell a little less
No correlation
- No pattern: the dots form a shapeless cloud and no line fits them
- Parking spaces near each bakery: busy and quiet shops alike, with or without parking
| What the dots do | Strength | What a forecast read off the line is worth |
|---|---|---|
| Hug the line (footfall and bread sales) | Strong | A reasonable estimate: Station Road's $5,340 a week |
| Follow the line in a wide band (loaf price) | Weak | A rough guide only: many bakeries sit far from the line |
| No line at all (parking) | None | No forecast: this variable tells Lena nothing about sales |
Moving together is not the same as causing: Lena's shops had their three best weeks of the year while her radio adverts were running. It looks as if the adverts sold the bread.
But the adverts ran in the three weeks before Christmas, when every bakery in town sells more. The link may be Christmas, a third factor behind both. Correlation shows that two things move together; it does not show that one causes the other.
So a comment on a scatter diagram has two halves: the direction (positive, negative or none) and the strength (how closely the dots sit to the line), and then what that means for the business. For Station Road: a strong positive correlation, so footfall is a good guide and $5,340 a week is a sensible figure to plan the staff and the first flour orders on.
Feeling unprepared for exams?
Get a clear study plan, practice with real questions, and know exactly where you stand before exam day. No more guessing.
How this comes up: With a table of past sales: plot the figures on a graph with both axes labelled, for two marks; construct a line of best fit through them, for one; draw (extrapolate) values for the next two years from that line, for two, one mark for each value read accurately.
With a case in which a business used regression: explain how it used simple linear regression to forecast, for two. The full answer names the independent and the dependent variable from the case.
With a scatter diagram: comment on the correlation, for two: its direction, then its strength or what it means for the business.
The two-mark pattern for regression
- Say what the tool does. It fits a straight line of best fit through past data on two variables, so one can be forecast from the other.
- Name the independent variable from the case. The figure the business already knew or measured: footfall outside each bakery.
- Name the dependent variable from the case. The figure it wanted to forecast: weekly bread sales.
- Finish with the forecast. It read the line at Station Road's own figure, 240 people an hour.
The trap: a general answer: 'It used past data to predict future sales' is true of every forecast, and it is one mark at most.
The second mark needs the two words, independent variable and dependent variable, each tied to the case's own figures. Swapping them round, sales as the independent variable, loses it.
Explain how Lena's Bakery used simple linear regression to forecast weekly bread sales for its Station Road shop.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.