Dependent Variable (placed on vertical axis: y)

• A dependent variable is a variable dependent on the value of another variable

Independent Variable (placed on horizontal axis: x)• The independent variable causes an

apparent change in, or affects the dependent variable

independent variable (x)

dependent variable (y)

Examples:

1) In a call centre, the number of customers serviced depends on the number of agents

2) At ski resort, the amount of sales, in $, depends on the amount of snow

3) The amount of bacteria on your hands depends on how often frequently you use hand sanitizer.

Experiment Independent Variable Dependent Variable

Is there a relationship between tv viewing and classroom grades? TV viewing Classroom Grades

Does a person's height depend on their foot length? Foot Length

(could go either way)

Height

What is the relationship between the world’s population and time? Time Population

Is there a relationship between the likelihood of cancer and the amount of red meat consumed?

Amount of Red Meat Consumed

Likelihood of Cancer

Is there a relationship between the number of words on a page versus the area of a book cover?

Area of Book Cover Number of Words on a Page

Is there a relationship in babies between crying and being held? Time Being Held Amount of Crying

A scatter plot shows a ____________ correlation when the pattern rises up to the right.This means that the two quantities increase together.

A scatter plot shows a ____________ correlation when the pattern falls down to the right.This means that as one quantity increases the other decreases.

A scatter plot shows _____ correlation when no pattern appears.Hint:If the points are roughly enclosed by a circle, then there is no correlation.

positive

negative

no

Strong or Weak Correlation?

Hint:To visualize this, enclose the plotted points in an oval.If the oval is thin, then the correlation is strong.If the oval is fat, then the correlation is weak.

If the points nearly form a line, then the correlation is ___________________.

If the points are dispersed more widely, but still form a rough line, then the correlation is _______________________.

strong

weak

a) Does age have a strong positive correlation with height? Explain.

b) Do you think the variables are placed appropriately on the axes?

c) Would weight vs. age show a strong positive correlation?

d) Can you think of a variable that does have a strong positive correlation with age?

e) Can you think of a variable that has a strong negative correlation with age?

…affectionately known as LOBF

All about the LOBF…All about the LOBF…

What is it?• shows a trend or pattern on a scatterplot• used to make predictions

How do I draw it?• models the trend/pattern• through as many points as possible• equal points above and below the line

• models the trend/pattern

Line of Best FitTo be able to make predictions, we need to model the data with a line or a curve of best fit.

Guide for drawing a line of best fit:1. The line must follow the ______________.2. The line should __________ through as many points as possible.3. There should be ____________________________ of points above and below the line.4. The line should pass through points all along the line, not just at the ends.

trendpass

equal

Which one of these is the best LOBF?

Which one of these is the best LOBF?

And what is wrong with the others?

#1

#3

#2

#4

Doesn’t

model trend

Line not in middle of

points

Wrong for all kinds

of reason

s!

• Return to front side of hand out and make lines of best fit on each of the given 6 graphs.

You can use LOBF’s to make predictions for

values that are not actually recorded or plotted.

InterpolationInterpolation• prediction involving a point within the set of data

Extrapolation

Extrapolation• prediction involving

a point outside the set of data

(line needs to be extended)

• Fill in blanks on handout

Height vs. Humerus

140

145150

155

160165

170

175

180185

190

20 22 24 26 28 30 32 34 36 38 40 42 44 46

Humerus (cm)

Hei

ght (

cm)

Using our height and humerus data…

Using our height and humerus data…

How tall would a person be that had a humerus

of 44 cm?

Is this interpolati

on or extrapolati

on?

Extend the

line!

181 cm tall181 cm tall

exptrapolationexptrapolation

Height vs. Humerus

140

145150

155

160165

170

175

180185

190

20 22 24 26 28 30 32 34 36 38 40 42 44 46

Humerus (cm)

Hei

ght (

cm)

Using our height and humerus data…

Using our height and humerus data…

How long would a person’s humerus be that

was 163 cm tall?

Is this interpolati

on or extrapolati

on?

28 cm long28 cm long

interpolationinterpolation

Makin’ sure you get it!

Makin’ sure you get it!

See bottom of handout

See bottom of handout

Correlation Between Science Class Attendance and Report Card Mark for Fifteen Students

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Number of Days Absent

Ma

rk (

%)

Points Versus Shots for Basketball Team

0

20

40

60

80

100

120

0 20 40 60 80

Basketball Shots

Nu

mb

er o

f P

oin

ts S

core

d