CO: Students will order scatterplots based on the strength of correlation. LO: Students
will describe a correlation as being “strong” or “weak”.
UNIT 4
Scatterplots and Correlation
CO: Students will order scatterplots based on the strength of correlation. LO: Students will describe
a correlation as being “strong” or “weak”.
Fri, Nov 13
Sit in your seat
 Everyone needs a shoulder partner!
 Open to p. 259
 Pull out your notebook
 Grab a half sheet

CO: Students will order scatterplots based on the strength of correlation. LO: Students will describe
a correlation as being “strong” or “weak”.
Scatterplot of Music Ranking




Rank the music in order from your favorite (#1) to
least favorite (#8).
Copy your shoulder partner’s rank onto your
paper, too.
Create a scatterplot of your data on the front!
Write your names big on the front.
 Make BIG points and write names BIG at
bottom!!
Answer p. 259 #1c-g as a pair (you’ll have to
walk around and look at other scatterplots)
CO: Students will order scatterplots based on the strength of correlation. LO: Students will describe
a correlation as being “strong” or “weak”.
Interpreting direction of a Scatterplot


Association is similar
to correlation!!!
Negative correlation:
pattern that moves from the
upper left to the lower right
Positive correlation:
pattern that moves from the
lower left to the upper right
Correlation Coefficient


Use the variable r
r is between -1 and 1



If the correlation is close to a positive line, r will be close to 1
If the correlation is close to a negative line, r will be close to -1
If the correlation is nothing near a line, r will be close to 0!
What to say when the r value is …
CO: Students will order scatterplots based on the strength of correlation. LO: Students will describe a correlation as being “strong
or “weak”.
Describe
the
following
scatterplots
and
estimate
the rvalues:
CO: Students will order scatterplots based on the strength of correlation. LO: Students will describe a
correlation as being “strong” or “weak”.
Line them up
Let’s make one big continuum on the board (by
taping the scatterplots up here) from strong
negative to strong positive.
 Line ‘em up!

CO: Students will order scatterplots based on the strength of correlation. LO: Students will describe a
correlation as being “strong” or “weak”.
How did we do?


Answer question p. 262 #4 with your shoulder
partner about the scatterplots on the board.
HW: p. 262 #5, p. 275 #11
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
Monday, Nov. 16


Groups: p. 264 #1-3
Check-in’s:
 1c
 1d
 2b
 2d
 3b
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
Interpreting Scatterplots
4 main things you need to talk about:

Overall pattern :
 Direction
(positive or negative association)
 Form (linear or non-linear- curved)
 Strength (how closely the points follow a clear form)

Striking deviations:
 Outlier
(outside the overall pattern)
 ???Clusters, Vary in strength, etc.
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
Linear vs. Non-Linear



Cloud/ Oval => “Linear”
Curved => “Non-Linear”
“Vary in Strength” … say that!
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
Outliers

Types of outliers
 Outliers
for the x variable only (Point C)
 Outliers for the y variable only (Point B)
 Outliers for both the x and y variables (Point E)
 Outliers that are only “outliers” when you look at
x and y at the same time (Points A and D)
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
Correlated or Caused


Correlation does not imply causation!
A correlation between two variables does not necessarily
mean one causes change in the other.
 Shark
attacks and ice cream sales…
 On a beach in Southern California the number of shark
attacks was strongly correlated with ice cream sales at
a little beach shack. Does this mean ice cream is
CAUSING shark attacks?
 What else could be going on here?
CO: Students will estimate the correlation coefficient of scatterplots and find residuals using a calculator.
LO: Students will state whether a linear equation will be the best model for a scatterplot in pairs.
Homework


p. 268 CYU,
p. 276 #12-13
CO: Students will find a linear regression line, calculate error in predictions and find residuals using a
calculator. LO: Students will state the difference between an error in prediction and a residual in pairs.
Tuesday, Nov 17


Everyone needs a calculator and a book
Pull out some paper for a few quick notes
CO: Students will find a linear regression line, calculate error in predictions and find residuals using a
calculator. LO: Students will state the difference between an error in prediction and a residual in pairs.
Scatterplot on Calculator


Add the data into lists
Height (x)
Shoe Size (y)
 Stat
50
5.5
64
9
70
12.5
62
7
Enter
 x into L1 and y into L2
Go to your stat plots
 2nd
y=
 Make sure it’s turned on
 Select the scatterplot


Set your window
Hit Graph
CO: Students will find a linear regression line, calculate error in predictions and find residuals using a
calculator. LO: Students will state the difference between an error in prediction and a residual in pairs.
Least-Squares on Calculator (Line of Best Fit)
1.
Add the data into lists
a)
x into L1 and y into L2
2.
STAT, CALC, #8 (LinReg a+bx)
3.
Add this to put it in y=:
VARS, , Y-VARS, FUNCTION, Y1
1.
2.
Then the regression line is entered
into your y= and the values for a
and b are given to you. (When
you write it down, round to 2
decimal places)
If you turn on the scatterplot, you
can see the scatterplot and the line
of regression. You will have to set
up a window that makes sense!!!
Height (x)
Shoe Size (y)
50
5.5
64
9
70
12.5
62
7
CO: Students will find a linear regression line, calculate error in predictions and find residuals using a
calculator. LO: Students will state the difference between an error in prediction and a residual in pairs.
Interpreting the regression line
The regression line:
𝑦 =.33x −11.61
“Interpret the slope and y-intercept”


Height (x)
Shoe Size (y)
50
5.5
64
9
70
12.5
62
7
The slope of .33 tells us that for every .33 increase in shoe
size someone will get 1 inch taller.
The y-intercept is what shoe size will equal when height is 0.
Do they make sense? Why/why not?
CO: Students will find a linear regression line, calculate error in predictions and find residuals using a
calculator. LO: Students will state the difference between an error in prediction and a residual in pairs.
Turn to p. 282


Groups: #1-3
Check-in’s:
 1a
 1c
 1d
 1e
 2b
 3b
(Hint, i. wants you to use your GRAPH of the line,
ii. wants you to use your EQUATION of the line!)
CO: Students will find a linear regression line, calculate error in predictions and find residuals using a
calculator. LO: Students will state the difference between an error in prediction and a residual in pairs.
Error in prediction vs. Residual
Using the regression equation :
Error in prediction/Residual
= observed value – predicted value

Error in prediction is used when the particular
type of car was not in the original data set.
 Residual is used when the particular type of car
was in the original data set.

CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
Error in prediction vs. Residual


Which point has the highest
residual?
Which point has the highest error
in prediction?


Where are the residuals positive?


Above the line
Where are they negative?


Trick question! None of the points!
Below the line
Where are the residuals 0?

ON the line
CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
Block, Nov. 18-19

1.
2.
3.
Warm-up:
How can you find a residual from a scatterplot?
How can you find a residual from an equation?
What’s the difference between an error of
prediction and a residual?
CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
Now for a little help Interpreting

Whenever it asks you to “interpret something in
context,” think about the term is using math, and
then substitute in the variables of the problem!
CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
What does the residual mean?

What is the equation for finding a residual?
 Residual
= Observed – Predicted
The residual shows how much higher or lower a
value is than was predicted.
 Sample sentence:
“The residual shows that _______ is ________

y-variable
residual number
higher/lower than what was predicted.”
positive
/ negative
(above line) / (below line)
CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
Example



Assume for this table that we find a residual of 4.23:
Years
Number of Birds
…
…
…
…
…
…
What does the residual mean in context?
“The residual shows that the number of birds is 4.23
higher than what was predicted.”
What does the slope mean?


What does the slope mean “in context” or “in terms
of the problem.”
What is the equation for finding a slope?
 Slope
=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
The slope shows how much the y- value changes
when the x- variable is increased by 1.
 Sample sentence:
“The slope shows that for every ______ that the

denominator
___ increases, the ____ increases/decreases by ___.
X-variable
y-variable
numerator
CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
Example




Assume for this table that we find a slope of 27:
Years
Number of Birds
…
…
…
…
…
…
What does the slope mean in context?
The slope shows that for every 1 that the years increase
by, the number of birds increases by 27.
The slope shows that for every 1 year that passes by,
there are 27 more birds.
CO: Students will practice interpreting slopes and residuals in context. LO: Students will interpret slopes
and residuals in context using fill-in-the blanks.
Practice

p. 285 CYU (a-c)

4.2 WS
CO: Students will create scatterplots and regression lines on their calculators. LO: Students will interpret
slopes and residuals in context using fill-in-the-blanks.
Monday, Nov. 30
Warm Up
1.
Explain what the slope means in context, given the
Ounces of Water
slope of 2.33. Minutes
2.
If the residual is -0.846, explain what that means.
(Hint: You need the sentence starters from before break!)

……..
………
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Warm Up: Tuesday, Dec. 1
The regression line:
𝑦 =.33x −11.61
Height (x)
Shoe Size (y)
50
5.5
64
9
70
12.5
62
7
Given the above information:
a)
Predict the shoe size of a person whose height is
55 inches.
b)
Find the residual for x = 64.
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Centroid

The centroid is the point (𝑥, 𝑦)
is the mean of all the x’s
 𝑦 is the mean of all the y’s
𝑥

The linear regression line crosses through the centroid
point!
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Centroid

10
11
13
15
16
31
34
37
38
45
Find the linear regression line of this data
𝑦

= 1.92𝑥 + 12
Find 𝑥 (the mean of all the x’s)


𝑥 =13
Find 𝑦 (the mean of all the y’s)


Centroid:
(13, 37)
𝑦 = 37
Check to see if the line goes through the centroid by
plugging it in for x and y and seeing if it is equal!
37 = 1.92 ∙ 13 + 12
37 = 36.96
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Influential Point: p. 287


Read the bottom paragraph
Pairs: #3
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Think/Pair Share

p. 290 Summarize the Math
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Influential Point


Go over how to delete a point out of the list, and
recalculate the correlation
If the correlation doesn’t change, is it influential?
CO: Students will determine if a point is influential. LO: Students will describe the effect that an influential
point has on the correlation.
Homework

p. 307 #3, 5
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Block Day, Dec. 2 and 3
Warm Up:
p. 305 #1
Friday is your EO #5 assessment!!!
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Correlation Coefficient
Which has a stronger
correlation?

TRICK QUESTION!
They are the same graph…
With different scales on
the axes!
Our eyes are NOT very
good judges of how strong
a linear relationship is! So
let’s learn how to calculate r!
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Calculating Correlation
You can calculate r at the same time as you do a
linear regression line if you do this step first:
1) Go to catalogue (2nd 0)
2) Go to DiagnosticOn
3) Press enter to turn it on
4) Now proceed to calculate LinReg
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Now it’s Your Turn!
Mins of HW
Quiz Scores
38
41
56
63
59
70
64
72
74
84
45
50
Find on your Calculator:
1)
Scatterplot
(Window: 0 – 80, 0 –
100)
1)
Linear Regression Line
2)
Correlation (r)
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Now it’s Your Turn!
Mins of HW
Quiz Scores
38
41
56
63
59
70
64
72
74
84
45
50
Find on your Calculator:
 Scatterplot
(Window: 0 – 80, 0 – 100)
 Linear Regression Line
y = 1.2x – 3.84
 Correlation (r)
r = 0.995
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Scatterplot
(15, 85)
I’m adding two
points. Are either
of them influential?
Data
r
Original
.995
with(5,2.5)
(5, 2.5)
with(15,85)
Add (5, 2.5) to your lists and re-calculate r.
Then delete (5, 2.5) and add (15, 85) to re-calculate r
See which one influences the data the most!
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Scatterplot
Data
r
Original
.995
with(5,2.5)
.999
with(15,85)
.129
(15, 85)
(5, 2.5)
So you can call (5 , 2.5) an OUTLIER, but it is NOT an
“influential point.”
(15, 85) is an “influential point.”
What does it mean to be an influential point?
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Definition of INFLUENTIAL POINT

An influential point is a point that strongly influences
the value of r.
 That
is, if the point is removed from the data set, the
value of r changes quite a bit.
 It is not influential if it’s far away from the other points.
It’s influential, if it is far away from where the linear
regression would lie.
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Homework
p. 298 CYU a-d, p. 310 #6a-d
 p. 305 #2, p. 316 #18


Friday is your Assessment on EO 5!!!
CO: SWBAT calculate the correlation on their calculators. LO: SWBAT list the steps for finding correlation
saying “first, then, last.”
Mon, Dec. 1


Welcome Back! Hope you had an awesome break!
Warm-up: p. 294 #4 and 6b