Topics
7. Bivariate data analysis
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AustraliaNSW
Year 12

7.04 Lines of best fit

Lesson
Worksheet
Practice
Worksheet
Lines of best fit
1

For each data set below, choose the graph that shows the most appropriate line of best fit.

a

Graph 1

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Graph 3

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Graph 2

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Graph 4

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b

Graph 1

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Graph 3

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Graph 2

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Graph 4

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2

Draw an approximate line of best fit by hand for the scatterplots below:

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3

Determine whether the following graphs show a negative relationship between the two variables:

a
b
c
Equations of lines of best fit
4

The equation of the line of best fit is of the form y=mx + c. For the given scatterplot, describe the likely value of m.

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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

Find the equation of your line of best fit.

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6

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

Find the equation of your line of best fit.

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7

Engineers measure the positions of various projectiles \left(x\right) in metres at different times \left(t\right) in seconds.

They calculate the line of best fit to be \\ x = 4.96 t + 50.96.

a

What was the average velocity of the projectiles?

b

What was the average starting position of the projectiles?

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8

Scientists record the number of aphids \left(A\right) in areas with different numbers of ladybeetles \left(L\right) in the scatterplot below.

They calculate the line of best fit to be \\ A = - 4.01 L + 3976.98.

a

How much does the average aphid population change by with each extra ladybeetle? Give your answer to the nearest aphid.

b

What is the average aphid population of a region with no ladybeetles? Give your answer to the nearest aphid.

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A
9

The temperature \left(T\right), in degrees celsius, of cups of coffee is measured at different times (t seconds) after being made.

The line of best fit is calculated to be \\ T = - 0.09 t + 22.47. According to the line of best fit:

a

What was the average rate of change of the temperature of the coffee?

b

What was the average initial temperature?

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10

The life expectancy \left(E\right), in years, of individuals at different annual incomes \left(I\right), per \$1000, is plotted below.

The line of best fit is calculated to be \\ E = 0.09 I + 72.55.

a

By how much does average life expectancy change for each \$1000 of annual income?

b

What is the average life expectancy of someone who earns no income?

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Predictions
11

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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12

The following scatter plot graphs data for the number of people in a room and the room temperature collected by a researcher.

a

Sketch the line of best fit for this data.

b

Use your line of best fit to estimate the room temperature when there are:

i

35 people in the room

ii

100 people in the room

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\text{People}
20\degree \text{C}
22\degree \text{C}
24\degree \text{C}
26\degree \text{C}
28\degree \text{C}
30\degree \text{C}
32\degree \text{C}
34\degree \text{C}
36\degree \text{C}
\text{Temperature}
13

The following scatter plot graphs data for the number of copies of a particular book sold at various prices:

a

Sketch the line of best fit for this data.

b

Use your line of best fit to find the number of books that will be sold when the price is:

i

\$33

ii

\$18

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\text{Price}
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\text{Sales}
14

The following scatter plot graphs data for the number of copies of a particular book sold at various prices.

a

Sketch the line of best fit for this data.

b

Use the line of best fit to find the number of books that will be sold when the price is:

i

\$33

ii

\$18

c

Is the relationship between the price of the book and the number of copies sold positive or negative?

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\text{Price}
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\text{Copies}
15

The following scatter plot graphs data for the number of ice blocks sold at a shop on days with different temperatures.

a

Sketch the line of best fit for this data.

b

Use your answer line of best fit to estimate the number of ice blocks that will be sold on a:

i

31 \degree \text{C} day

ii

42 \degree \text{C} day

c

Does the number of ice blocks sold increase or decrease as the temperature increases?

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\text{Temperature}(\degree \text{C})
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\text{Ice blocks}
16

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}
17

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}
Technology
18

Use technology to find the line of best fit for the data below. Write the equation of the line in the form t = m p + c with the coefficient and constant term to the nearest two decimal places.

p34312239131928242839
t-6-6-4-11-4-4-9-4-5-8
19

Draw the line of best fit using technology for the scatterplots below:

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20

Consider the following data:

x1123354521
y7-21111112162027
a

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

b

A scatterplot of the points in the table is provided. Using the result of part (a), draw an approximate line of best fit.

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21

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
d
x2231544353
y9744151313121613
e
x29273136223839311715
y-9-8-7-10-6-10-9-9-3-2
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Outcomes

MS2-12-2

analyses representations of data in order to make inferences, predictions and draw conclusions

MS2-12-7

solves problems requiring statistical processes, including the use of the normal distribution and the correlation of bivariate data

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