← VCE Data Analytics U3O1

Trendlines on a chart

A line fitted through a chart's points that shows the overall direction of the data. A chart tool can add one with its equation, and the R-squared value shows how well it fits.

Part of: VCE Data Analytics - U3O1 - Data Analytics — Module 91, VCE Data Analytics - U4O1 - Development and Evaluation — Module 36, 9-10 Digital Technologies: Analysing and visualising data — Module 7, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 42

Understanding Trendlines on a chart in VCE Data Analytics U3O1

What it does: Here the slope is 2.5, so y goes up by 2.5 each time x increases by 1. The 10 is where the line crosses the y axis. An R-squared of 0.96 is close to 1, so the points sit very near the line and the trendline describes the data well. A trendline is fitted through the points to show the general direction. It does not pass through every point. A positive number in front of x means y rises as x rises. A negative number means y falls. The number multiplied by x is the slope. It is how much y changes when x goes up by 1.

Common mistakes: A scatter plot needs two columns, x values and y values, so the range should be A2:B20. A single column gives no pairs of points to fit a trendline through. The equation of a straight trendline is y = m * x + b. The slope m multiplies x and the intercept b is added on the end.

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This module's key terms are also in a printable crossword (Modules 50–91) and word search (Modules 17–91).

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Learning
Duo
What does a trendline show on a scatter plot?
The exact value of every single pointThe overall direction of the data
Matches
y = -3x + 8 means the data is rising
↓
A negative slope means the trend goes down as x increases, not up. Rising data has a positive slope.
Applying
Meanings
Term
trendline
Meaning
A line fitted through a chart's points that shows the overall direction of the data. A chart tool can add one with its equation, and the R-squared value shows how well it fits.
Practice
=SLOPE(B2:B13,A2:A13)
Testing
Gaps
=(B2:B12,A2:A12)
Check Answer
Spots
1chart = Scatter(A2:A20)
2chart.addTrendline("linear")

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Quick Questions

1. What does a trendline show on a scatter plot?
A. The overall direction of the data ✓
B. The exact value of every single point
A trendline is fitted through the points to show the general direction. It does not pass through every point.
2. Which trendline slope means the values are going up as time goes on?
A. A negative slope, such as y = -2.5x + 10
B. A positive slope, such as y = 2.5x + 10 ✓
A positive number in front of x means y rises as x rises. A negative number means y falls.
3. A trendline's equation is y = 3x + 5. What does the 3 tell you?
A. y is always equal to 3
B. y goes up by about 3 for every 1 increase in x ✓
The number multiplied by x is the slope. It is how much y changes when x goes up by 1.
4. Which R-squared value shows the trendline fits the points best?
A. R² = 0.95 ✓
B. R² = 0.15
R-squared is between 0 and 1. The closer it is to 1, the better the line fits the data.
5. Where would you add a trendline in a spreadsheet chart?
A. Chart elements menu, then Trendline ✓
B. Sort the data from A to Z
Chart tools let you add a trendline from the chart elements or chart editor. You can also tick the options to show the equation and R-squared.

Match the Pairs

=SLOPE(B2:B20,A2:A20) → Finds the slope of the trendline, which is how much the y values change for each 1 step along x
=RSQ(B2:B20,A2:A20) → Gives the R-squared value, a number from 0 to 1 showing how well the trendline fits the points
A trendline equation in the form y = mx + b, where m is the slope that shows the direction of the trend → y = 2.5x + 10
A very high R-squared means the trendline fits the data closely → R² = 0.96
y = -3x + 8 means the data is rising → A negative slope means the trend goes down as x increases, not up. Rising data has a positive slope.
R² = 0.05 means the trendline fits perfectly → An R-squared near 0 means a poor fit. A perfect fit is close to 1.

Key Term

trendline
A line fitted through a chart's points that shows the overall direction of the data. A chart tool can add one with its equation, and the R-squared value shows how well it fits.

Fill in the Blanks

1. =SLOPE(B2:B12,A2:A12)
Hint: Type the function name that returns the steepness of the trendline.
2. =RSQ(B2:B12,A2:A12)
Hint: Type the function name that returns the R-squared fit value.
3. y = mx + b
Hint: Type the letter that stands for the slope in the trendline equation.
4. R-squared close to 1 means a strong fit
Hint: Type the number that R-squared gets close to for a nearly perfect fit.
5. A positive slope means the trend goes up
Hint: Type the direction the trendline heads when the slope is positive.

Spot the Error

Question 1
A chart = Scatter(A2:A20)
B chart.addTrendline("linear")
C chart.showEquation = true
Line A — A scatter plot needs two columns, x values and y values, so the range should be A2:B20. A single column gives no pairs of points to fit a trendline through.
Question 2
A m = SLOPE(B2:B20,A2:A20)
B b = INTERCEPT(B2:B20,A2:A20)
C y = m + x * b
Line C — The equation of a straight trendline is y = m * x + b. The slope m multiplies x and the intercept b is added on the end.
Question 3
A IF slope > 0 THEN
B trend ← "rising"
C ELSE IF slope < 0 THEN
D trend ← "steady"
E ELSE trend ← "flat"
Line D — A negative slope means the trendline goes down as x increases, so the trend is "falling". Line 4 should be trend ← "falling".
Question 4
A Trendline type: Linear
B Display equation: on
C Display R-squared: on
D R-squared = 1.93
E Fit: strong
Line D — R-squared always sits between 0 and 1, so 1.93 is impossible. A value like 0.93 shows a strong fit.
Question 5
A sales ← [10, 14, 19, 25]
B weeks ← [1, 2, 3, 4]
C slope ← SLOPE(weeks, sales)
D OUTPUT slope
Line C — SLOPE takes the y values first, then the x values. Sales (y) depend on weeks (x), so the call should be SLOPE(sales, weeks).

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