dependent variable (placed on vertical axis: y)
DESCRIPTION
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. Examples: - PowerPoint PPT PresentationTRANSCRIPT
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