2 - Scatter Plot Trends + Line of Best Fit.pdf

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Graphing Vocabulary

Match the words in the following word list to each of the seven definitions given below.

 Dependent Variable

 Extrapolation

 Independent Variable

 Interpolation

 Line of Best Fit

 Linear

 Non-Linear

Definition

When the points on a scatter plot appear to follow a straight line.

Notable Notes

The points do not need to form a perfectly straight line.

Non Examples Examples

Definition

The variable in an experiment that is controlled.

Notable Notes

Graphed on the x-axis.

Examples

Time

Non Examples

Depth of Water

Definition

The variable in an experiment that is measured or observed.

Notable Notes This is what you are most interested in

measuring in an experiment.

Graphed on the y-axis.

Non Examples

Time Examples

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Definition

Predicting a value outside of your data set.

Notes

Non Examples

How many visitors were there when it was 83o?

Examples

How many visitors were there

when it was 80o? Definition

When the points on a scatter plot appear to follow a curve or have no pattern at all.

Notes

Non Examples Examples

Definition

A straight line that models the trend shown by your data.

Notes

This can be used to make predictions based on your data.

Non Examples Examples

Definition

Predicting a value inside of your data set.

Notes

Non Examples

How many visitors were there when it was 104o? Examples

How many visitors were there

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0 2 4 6 8 10 12 14 16 18 20

0 20 40 60 80 100 120 140

Speed (km /h)

F u e l C o n s u m p ti o n ( L p e r 1 0 0 k m )

Scatter Plots & Trends

For each of the following graphs, circle any outliers, identify the independent and dependent variables, identify whether it is a linear or non-linear relationship, and state the trend.

a)

Independent Variable: ______________________________

Dependent Variable: ______________________________

Linear / Non-Linear

Trend:

b)

Independent Variable: ______________________________

Dependent Variable: ______________________________

Linear / Non-Linear

Trend:

c)

Independent Variable: ______________________________

Dependent Variable: ______________________________

Linear / Non-Linear

Trend: 0 20 40 60 80 100

0 5 10

Number of Cars Washed

M o n e y Ea rn e d 0 4 8

0 1 2 3 4 5 6

Height of Skateboard Ramp

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0 5 10 15 20 25 30

0 2 4 6 8 10 12

0 5 10 15 20 25 30 35 40

0 2 4 6 8 10 12

0 10 20 30 40 50 60 70 80

0 2 4 6 8 10 12

0 20 40 60 80 100 120

0 2 4 6 8 10 12

0 10 20 30 40 50 60 70 80 90 100

0 2 4 6 8 10 12

Line of Best Fit

1. For each of the following graphs, determine if the graph is linear or non-linear. If it is linear, draw a line of best fit.

a)

Linear / Non-Linear

b) c)

Linear / Non-Linear Linear / Non-Linear

d) e)

Linear / Non-Linear Linear / Non-Linear

A good line of best fit…

Follows the trend

Is in the middle of the data (same # of points above and below)

Extends from one end of the grid to the other

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2. The following table shows the number of students that have applied to Ontario Universities each year since 2004.

Year # of Students Applying

2004 71771

2005 73956

2006 76300

2007 80362

2008 83813

2009 84691

2011 89181

2012 90889

a) Identify the independent variable.

b) Identify the dependent variable.

c) What does the zig-zag on the x-axis mean?

d) What is one square worth on the x-axis?

e) What is one square worth on the y-axis?

f) How did the person making the graph decide where to put the point for 2011?

g) One of the points is plotted incorrectly. Which one is it? Correctly plot the point.

h) Draw in a line of best fit.

i) Using your line of best fit, predict the number of students that applied in 2016. Is this an example of interpolation or extrapolation?

j) Using your line of best fit, predict the number of students that applied in 2010. Is this an example of interpolation or extrapolation?

40000 50000 60000 70000 80000 90000 100000 110000 120000 130000

2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022

Year

#

of

S

tud

ent

s

App

ly

ing t

o O

nt

ar

io Univ

er

si

tie

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Scatter Plots, Trends, & Line of Best Fit Homework

1. The following scatter plot shows the average temperature of the ocean as a function of the latitude, in the southern hemisphere.

a) State the independent and dependent variables.

Independent:

Dependent:

b) State the trend shown by this graph.

c) Draw a line of best fit.

d) Predict the average temperature of the ocean at a latitude of 35oS. Is this an example of interpolation or extrapolation?

e) Predict the average temperature of the ocean at a latitude of 55oS. Is this an example of interpolation or extrapolation?

f) At what latitude would you expect the average temperature to be 2 oC? Is this an example of interpolation or extrapolation?

g) At what latitude would you expect the temperature to be 17 oC? Is this an example of interpolation or extrapolation?

Ocean Temperature (Southern Hemisphere)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

0 10 20 30 40 50 60 70 80 90

Latitude (S)

Te

mp

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2. The following graph represents the relationship between the final exam mark (%) and the number of hours of sleep that a student got before their exam.

a) Identify the independent variable. Justify your choice.

b) Identify the dependent variable. Justify your choice.

c) Label the x and y axes appropriately based on your answers from a) and b).

d) What does each square represent on the x-axis?

e) What does each square represent on the y-axis?

f) Fill in the following table of values using the graph:

g) State the trend shown by the graph. h) Draw a line of best fit and predict what

mark you think someone who got 4 hours of sleep should get. Is this an example of interpolation or extrapolation?

Number of Hours of Sleep

Final Exam Mark (%)

0 10 20 30 40 50 60 70 80 90 100

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3. The following table of values shows the height of a balloon versus time.

Time (s) Height (m)

2 5

4 7

6 10

8 13

10 18

12 21

14 24

16 25

18 27

20 30

a) Create a scatter plot.

b) State the trend shown by the graph.

c) Draw a line of best fit.

d) Predict the height of the balloon after 9 seconds.

e) Is your answer to d) an example of interpolation or extrapolation?

f) Predict how long it would take for the balloon to reach a height of 40 m.

g) Is your answer to f) an example of interpolation or extrapolation?

h) How high above the ground was the

balloon when it was released?

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Time (s)

H

e

ig

h

t

(m

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0 5 10 15 20

0 5 10 15 20

4. The following table shows the number of chin-ups that a student can do, compared to their age.

a) Determine the independent and dependent variables. Label them on the appropriate axes on the graph.

Independent:

Dependent:

b) Create a scatter plot of the data in the table.

c) State the trend shown by the graph.

d) Stacey can do 18 chin-ups. How old do you think she is?

e) Is your answer from d) an example of interpolation or extrapolation?

f) Tahir is 6 years old. How many chin-ups would you expect him to be able to do?

g) Is your answer from f) an example of interpolation or extrapolation?

ANSWERS:

1a] Independent: Latitude, Dependent: Temperature 1b] As the latitude increases, the temperature of the water decreases 1d] (Answers Will Vary) 12.5 oC

1e ] (Answers Will Vary) 5.3 oC 1f] (Answers Will Vary) 64 oS 1g] (Answers Will Vary) 23 oS 2a] Hours of Sleep – this is the variable that you would have some control over 2b] Final Exam Mark – this is what we are more interested in measuring 2c] X-Axis: Hours of Sleep, Y-Axis: Final Exam Mark

2d] 1 hour of sleep 2e] 5% on the exam 2f] (0, 30), (1, 92), (2, 40), (2.4, 45), (3, 55), (5, 55), (5, 65), (6, 70), (8, 84), (9, 25), (10, 95), (11, 90) 2g] As the hours of sleep increases, the final exam mark increases 2h] (Answers Will Vary) 56%, Interpolation 3b] As time increases, the height of the balloon increases 3d] (Answers Will Vary) 15.2 m 3e] Interpolation 3f] (Answers Will Vary) 26 sec 3g] Extrapolation 3h] (Answers Will Vary) 2 m

4a] Independent: Age, Dependent: Number of Chin-Ups 4c] As age increases, the number of chin-ups that a student can do increases 4d] (Answers Will Vary) 19.5 years old 4e] Extrapolation 4f] (Answers Will Vary) 1 chin-up 4g] Extrapolation

Age Number of

Chin-Ups

10 8

11 8

12 8

13 11

15 13

14 11

13 9

17 14

13 10

14 12

16 14

17 16

10 7

16 15

10 7

Figure

Updating...

References