To view this presentation, you'll need to enable Flash.

Show me how

After you enable Flash, refresh this webpage and the presentation should play.

Loading...

PPT – Chapters 8 and 9: Correlations Between Data Sets PowerPoint presentation | free to download - id: 70bdf4-MjM1O

The Adobe Flash plugin is needed to view this content

View by Category

Presentations

Products
Sold on our sister site CrystalGraphics.com

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Chapters 8 and 9 Correlations Between Data Sets

- Math 1680

Overview

- Scatter Plots
- Associations
- The Correlation Coefficient
- Sketching Scatter Plots
- Changes of Scale
- Summary

Scatter Plots

- Often, we are interested in comparing two related

data sets - Heights and weights of students
- SAT scores and freshman GPA
- Age and fuel efficiency of vehicles
- We can draw a scatter plot of the data set
- Plot paired data points on a Cartesian plane

Scatter Plots

- Scatter plot for the heights of 1,078 fathers and

their adult sons - From HANES study

Scatter Plots

- What does the dashed diagonal line represent?
- Find the point representing a 5'3¼" father who

has a 5'6½" son

Scatter Plots

- What does the vertical dashed column represent?
- Consider the families where the father was 72"

tall, to the nearest inch - How tall was the tallest son?
- Shortest?

Scatter Plots

- Was the average height of the fathers around 64,

68 or 72? - Was the SD of the fathers heights around 3", 6"

or 9"?

Scatter Plots

- The points form a swarm that is more or less

football-shaped - This indicates that there is a linear association

between the fathers heights and the sons heights

Scatter Plots

- Short fathers tend to have short sons, and tall

fathers tend to have tall sons - We say there is a positive association between

the heights of fathers and sons - What would it mean for there to be a negative

association between the heights?

Scatter Plots

- Does knowing the fathers height give a precise

prediction of his sons height? - Does knowing the fathers height let you better

predict his sons height?

Scatter Plots

- We will generally assume the scatter plots are

football-shaped - Association is linear in nature
- Each data set is approximately normal

Scatter Plots

- Key features of scatter plots
- Given two data sets X and Y,
- The point of averages is the point (?x, ?y)
- The average of a data set is denoted by µ (Greek

mu, for mean) - The subscript indicates which set is being

referenced - It will be in the center of the cloud
- Due to the normal approximation, the vast

majority (95) of the cloud should fall within 2

SDs less than and greater than average for both

X and Y

Scatter Plots

Associations

- When given a value in one data set, we often want

to make a prediction for the other data set - We call our given value the independent variable
- We call the value we are trying to predict the

dependent variable

Associations

- If there is indeed a relationship between the two

data sets, we can say various things about their

association - Strong Knowing X helps you a lot in predicting

Y, and vice versa - Weak Knowing X doesnt really help you predict

Y, and vice versa - Positive X and Y are directly proportional
- The higher in one you look, the higher in the

other you should be - Negative X and Y are inversely proportional
- The higher in one you look, the lower in the

other you should be

Associations

- Positive associations
- Study time/final grade
- Height/weight
- SAT score/GPA
- Clouds in sky/chance of rain
- Bowling practice/bowling score
- Age of husband/age of wife

- Negative associations
- Age of car/fuel efficiency
- Golfing practice/golf score
- Dental hygiene/cavities formed
- Pollution/air quality
- Speed/mile time

Associations

- What kind of association is this?

Associations

- What kind of association is this?

Associations

- Remember that even a very strong association does

not necessarily imply a causal relationship - There may be a confounding influence at play

The Correlation Coefficient

- While strong/weak and positive/negative give a

sense of the association, we want a way to

quantify the strength and direction of the

association - The correlation coefficient (r) is the statistic

which accomplishes this

The Correlation Coefficient

- The correlation coefficient is always between 1

and 1 - A positive r means that there is a positive

association between the sets - A negative r means that there is a negative

association between the sets - If r is close to 0, then there is only a weak

association between the sets - If r is close to 1 or 1, then there is a strong

association between the sets

The Correlation Coefficient

- The following plots have and

, with 50 points in them - The only difference between them is the

correlation coefficient - Note how the points fall into a line as r

approaches 1 or 1

(No Transcript)

The Correlation Coefficient

- To calculate r
- Find the average and SD of each data set
- Multiply the data sets pairwise and find the

average - The correlation is the average of the product

minus the product of the averages, all divided by

the product of the SDs

The Correlation Coefficient

X Y

1 5

3 9

4 7

5 1

7 13

The Correlation Coefficient

- Compute r for the following data

X Y

1 2

2 1

3 4

4 3

5 7

6 5

7 6

X Y

1 3

3 7

4 9

5 11

7 15

1

0.8214

The Correlation Coefficient

- Estimate the correlation

The Correlation Coefficient

- Estimate the correlation

Sketching Scatter Plots

- The SD line is the line consisting of all the

points where the standard score in X equals the

standard score in Y - zX zY
- To sketch the SD line, draw a line bisecting the

long axis of the football shape - Note that the SD line always goes through the

point of averages

Sketching Scatter Plots

- Given the five-statistic summary (averages, SDs,

and correlation) for a pair of data sets, we can

sketch the scatter plot - Plot the point of averages in the center
- Mark two SDs in both directions, on both axes
- Plot the point 1 SD above average for both data

sets - draw a line connecting this point and the point

of averages - This is the SD line
- Draw an ellipse with the SD line as its long axis

- Ellipse should go just beyond the 2 SD marks in

all directions - The value of r determines how oblong the ellipse

is

Sketching Scatter Plots

- A study of the IQs of husbands and wives obtained

the following results - Husbands average IQ 100, SD 15
- Wives average IQ 100, SD 15
- r 0.6
- Sketch the scatter plot

Changes of Scale

- The correlation coefficient is not affected by

changes of scale - Moving adding the same number to all of the

values of one variable - Stretching multiplying the same positive number

to all the values of one variable - Would r change if we multiplied by a negative

number? - The correlation coefficient is also unaffected by

interchanging the two data sets

Changes of Scale

Changes of Scale

Changes of Scale

- Compute r for each of the following data sets

X Y

0 8

4 9

6 10

8 12

12 6

X Y

0 2

2 3

3 4

4 6

6 0

r -0.15

Summary

- The relationship between two variables, X and Y,

can be graphed in a scatter plot - When the scatter plot is tightly clustered around

a line, there is a strong linear association

between X and Y - A scatter plot can be characterized by its

five-statistic summary - Average and SD of the X values
- Average and SD of the Y values
- Correlation coefficient

Summary

- When the correlation coefficient gets closer to 1

or 1, the points cluster more tightly around a

line - Positive association has a positive r-value
- Negative association has a negative r-value
- Calculating the correlation coefficient
- Take the average of the product
- Subtract the product of the averages
- Divide the difference by the product of the SDs

Summary

- The correlation coefficient is not affected by

changes of scale or transposing the variables - Correlation does not measure causation!

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Presentation Removal Request Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Chapters 8 and 9: Correlations Between Data Sets" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!