Warm Up- Quiz today
1.
Plot the data. What kind of
growth does it exhibit? (plot by hand but
you may use calculators to confirm answers.)
2.
3.
4.
5.
6.
Use logs to transform the data
into a linear association and plot
it.
Find the LSRL equation on Log Y
and X.
Graph the line from #3
Determine the exponential
equation (model) for log of the
original dataset. (Form
y=c(10^kx) where c and k are
constants.
Compare/Discuss Homework
with partner and turn in.
Shake #
# of m&ms
1
1
2
2
3
4
4
7
5
12
6
18
7
24
8
37
9
54
10
78
11
108
12
146
Warm Up
1.
Plot the data. What kind of
growth does it exhibit? (plot by hand but
you may use calculators to confirm answers.)
2.
3.
4.
Use logs to transform the data
into a linear association and plot
it.
Find the LSRL equation on Log Y
and X. Write the equation and
Draw this line on your second
(linear graph)
Determine the exponential
equation (model) for the original
dataset. (Form y=c(10^kx) where
c and k are constants.
Age #
Savings
5
12
10
78
15
506
20
3,300
25
21,000
30
90,000
Get ready…you or your partner
need to…

Take out a sheet of binder paper and
cut in half. Half for you half for your
partner.

Label with name, date period on top
right corner.
AP Statistics, Section 4.2, Part 1
3
Reading Quiz 4.2
1.
2.
Correlation and regression are used for what
kind of relationships?
Are correlation, r, and least squares regression
line resistant or not?
3.
What do we call a ‘hidden’ variable that is not
among the explanatory or response variables in
a study and yet may influence the interpretation
of relationships among those variables?
4.
A high correlation, r, does imply causation.
True or False.
4
Reading Quiz 4.2
1.
2.
Correlation and regression are used for what kind of
relationships?
_____________is the use of a regression line for prediction
far outside the domain of values of the explanatory variable x
that you used to obtain the line or curve. Such predictions are
often not accurate.
3.
What do we call a ‘hidden’ variable that is not among the
explanatory or response variables in a study and yet may
influence the interpretation of relationships among those
variables?
4.
Correlation, r, and least squares regression line are not
resistant. True or False
Correlations based on averages are usually too ______ when
applied to individuals.
5
5.
Key to Reading Quiz 4.2
1.
2.
3.
4.
5.
Linear Relationships
Extrapolation
Lurking Variable
True
High
AP Statistics, Section 4.2, Part 1
6
Section 4.2.1
Cautions
AP Statistics
Cautions, Part 1
Regression and correlation describe only
linear relationships
 Not resistant measures

AP Statistics, Section 4.2, Part 1
8
Cautions, Part 2
Extrapolation is the use of a regression line for
prediction far outside the domain of values of
the explanatory variable x that you used to
obtain the line or curve.
 Such predictions are often not accurate.
 Examples

 Keeping
track of a child's growth
 Speed continues to decrease when running the
mile.
AP Statistics, Section 4.2, Part 1
9
Cautions, Part 3

Lurking Variable is a variable that is not
among the explanatory or response
variable in a study and yet may influence
the interpretation of relationships among
those variables.
AP Statistics, Section 4.2, Part 1
10
Basketball example
Piston Points vs. Piston Fouls
P
o
i
n
t
s
Fouls
Since we have a positive slope we say that for every 4.28 fouls the team gets a
point. So the more fouls the more points???
Lurking Variable?
Lurking variable: Playing Time
AP Statistics, Section 4.2, Part 1
11
Piston Minutes vs. Piston Points
AP Statistics, Section 4.2, Part 1
12
Piston Minutes vs. Piston Fouls
AP Statistics, Section 4.2, Part 1
13
Another Example
In the 1600-1800s the number of English
Ministers in America increased
 The consumption of rum increased
 So the Ministers caused the people to
drink more rum?
 Lurking Variable?

 Increase
in population.
AP Statistics, Section 4.2, Part 1
14
Clustering can allow us to see
correlation that exist within subgroups



The more
education the get
the lower the
salary???
So drop out of
school now???
Solid circles
indicate Phd.
Economist Education and Salary
S
a
l
a
r
y
Years of Education
AP Statistics, Section 4.2, Part 1
15
Can the number of students in
math classes be used to predict the
number enrolled?
Maybe
the
number
of
required
math
classes
changes
AP Statistics, Section 4.2, Part 1
17
Good residual plot?
AP Statistics, Section 4.2, Part 1
18
Residuals vs. Time. Different
conclusion?
AP Statistics, Section 4.2, Part 1
19
Caution, Part 4
Avoid using averaged data.
 Correlations based on averages are
usually too high when applied to
individuals.
 Example

 Take
the mean height of my six class vs. all
180 heights from all students.
 Don’t use average data` when you can use
raw data.
AP Statistics, Section 4.2, Part 1
20
Assignment

Exercises: 4.27, 4.28, 4.31, 4.32
AP Statistics, Section 4.2, Part 1
21