Topics
22. Statistics
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iGCSE (2021 Edition)

22.15 Lines of best fit

Lesson
Worksheet
Practice
Worksheet
Line of best fit
1

Draw an approximate line of best fit by hand for each of the the scatter plots below:

a
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20
x
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y
b
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x
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y
c
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x
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y
d
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y
2

The following scatter plot shows the data for two variables, x and y:

a

Sketch the line of best fit for this data.

b

Use your line of best fit to estimate the value of y when:

i

x = 4.5

ii

x = 9

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y
3

The following scatter plot graphs data for the number of balls hit and the number of runs scored by a batsman:

a

Sketch the line of best fit for this data.

b

Use the line of best fit to estimate the number of runs scored by the batsman after hitting:

i

27 balls

ii

66 balls

c

Is the relationship between the two variables positive or negative?

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\text{Balls Hit}
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\text{Runs}
4

The average monthly temperature and the average wind speed, in knots, in a particular location was plotted over several months. The graph shows the points for each month’s data and their line of best fit:

Use the line of best fit to approximate the wind speed on a day when the temperature is 5\degree \text{C}.

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\text{Temperature}(\degree \text{C})
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\text{Speed}
Equation of a line of best fit
5

Consider the following scatter plot:

a

Is the relationship between the x and y variables positive or negative?

b

Sketch the line of best fit for this data.

c

Which of the following could be the equation for the line of best fit:

A
y = 2 - 3 x
B
y = 3 x + 2
C
y = - 3 x - 2
D
y = 3 x - 2
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y
6

Consider the following scatter plot:

a

Is the relationship between the x and y variables positive or negative?

b

Which of the following could be the equation for the line of best fit:

A
y = - 4 x - 4
B
y = 44 + 4 x
C
y = - 4 x + 44
D
y = 4 x - 4
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x
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y
7

Use technology to find the line of best fit for the sets of data below. Write the equation with the coefficient and constant term to the nearest two decimal places.

a
x24371931322214302340
y-7-8-3-6-9-8-2-8-8-12
b
x718169161988127
y16.293.567.2512.118.253.2612.512.510.3314.29
c
x44394150455548544443
y2.291.573.863.144.434.863.864.714.294.14
8

Several cars underwent a brake test and their age, x (in years), was measured against their stopping distance, y (in metres). The scatter plot shows the results and a line of best fit that approximates the positive correlation:

a

According to the line, what is the stopping distance of a car that is 6 years old?

b

According to the line, what is the stopping distance of a car that is 10 years old?

c

Using the information found above, determine the gradient of the line of best fit.

d

State the value of the vertical intercept of the line.

e

Use the line of best fit found to estimate the stopping distance of a car that is 4.5 years old.

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\text{Age}
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\text{Distance}
9

The distance of several locations from the equator and their temperature on a particular day is measured. The values are presented on the following scatter plot:

a

Determine whether the following could be the equation of the line relating distance \left(x\right) and temperature \left(y\right):

A
y = - 0.005 x + 49
B
y = - 0.005 x - 49
C
y = 0.005 x + 49
D
y = 0.005 x - 49
b

Estimate the distance from the equator, x, if the temperature is 30.59 \degree \text{C}.

10

Find the equation of the line of best fit on the scatter plot shown:

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y
11

Consider the scatter plot shown:

a

Find the equation of the line of best fit.

b

Use the line of best fit to approximate the value of y for x = 6.9.

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x
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y
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Outcomes

0580C9.8

Draw, interpret and use lines of best fit by eye.

0580E9.8

Draw, interpret and use lines of best fit by eye.

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