Scatterplots and Trend Lines

Lecture 9.1 & 9.2 - Scatterplots & Trend Lines

By Gabe Geering

Scatterplot

→​ shows the relationship between bivariate data

Yay for "when are we gonna use this stuff?"

Bivariate Data

→​ data with two variables, most likely x and y. Also known as pairs of numerical data.

I scream, you scream, we all scream for ice cream or for our lives if the temperature rises any higher in that data...

Association

→​ any relationship between two measured quantities that renders them statistically dependent

You know, like the more homework you do... the better you do on a test... right? RIGHT?

scatterplot nearly forms a line​

scatterplot forms into shape that's not line and a different type of function

Non-linear Association

​

​TYPES OF ASSOCIATION

Linear Association

​

​as x increases, y increases

Positive Association

​

as x increases, y decreases

Negative Association

​

​no relationship between x

No Association

​

​TYPES OF LINEAR ASSOCIATION

We call linear association a "correlation"

Multiple Choice

Which scatter plot shows a linear relationship between x and y?

• Graph A
• Graph B
• Graph C
• Graph D

Multiple Choice

Describe the association for the graph.

• Linear and Positive

• Linear and Negative

• Non-Linear and No Association

• Non-Linear and Positive

• Non-Linear and Negative

Multiple Choice

The association value for this graph will indicate a

• Negative, non-linear

• Postive, Linear

• Negative, Linear

• Positive, non-linear

Multiple Choice

Describe the correlation in the graph shown.

• Linear and Negative

• Linear and Positive

• Non-linear Negative

• Non-linear and Positive

Multiple Choice

Describe the association for the graph.

• Linear and Positive

• Linear and Negative

• Non-Linear and Negative

• Non-Linear and Positive

• Non-Linear and No Association

Multiple Choice

Describe the Association for the graph.

• Linear and Negative

• Linear and Positive

• Non-Linear and No Association

• Non-Linear and Positive

• Non-Linear and Negative

Multiple Choice

Describe the association for the graph.

• Linear and Negative

• Linear and Positive

• Non-Linear and No Association

• Non-Linear and Positive

• Non-Linear and Negative

Multiple Choice

Which scatterplot does NOT suggest a linear relationship between x and y?

Multiple Choice

Which best describes the form of this scatterplot?

• linear positive

• non-linear

• linear negative

• no association

Multiple Choice

Describe the association of the scatter plot.

• Linear; positive association

• Linear; negative association

• Non-linear

• No association

​TYPES OF CORRELATION

​The closer the scatterplot is to creating a line, the stronger the correlation, meaning the likelihood that the variables are related is much higher. We want stronger correlations for better predictions.

Multiple Choice

Identify the type of association.
The number of workers and the time it takes to build a house.

• Positive correlation
• Negative correlation
• No correlation

Multiple Choice

Identify the type of association.
The color of your hair and the brand of toilet paper you use.

• Positive correlation
• Negative correlation
• No correlation

Multiple Choice

Identify the type of association.
The amount of gas left in the car and the number of miles driven.

• Positive
• Negative
• None

Multiple Choice

Identify the type of association.
The type of phone you use and the number of siblings you have.

• Positive
• Negative
• None

Multiple Choice

Identify the type of association.

The amount of junk food you eat and your friend's height

• Positive

• Negative

• None

Multiple Choice

Describe the relationship between the variables.

• A) Weak positive correlation

• B) Weak negative correlation

• C) Strong positive correlation

• D) Strong negative correlation

Multiple Choice

Describe the correlation in the graph shown.

• A) Strong Negative

• B) Strong Positive

• C) Weak Negative

• D) No Correlation

Multiple Choice

• Positive, strong
• Positive, weak
• Negative, strong
• Negative, weak

Multiple Choice

• Positive, strong
• Positive, weak
• Negative, strong
• Negative, weak

Multiple Choice

• Positive, strong
• Positive, weak
• Negative, strong
• Negative, weak

Trend Line

→​ a line drawn through a

scatterplot to represent the data. It can be used to make predictions within the data or outside the data.​

How trendy... we can draw these lines ourselves or have an algorithm in a calculator do it for us 😏

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 180 pages. 

• 12 chapters
• 15 chapters
• 18 chapters
• 21 chapters

Multiple Choice

Based on the graph, if Joe earned $400, how many hours did he work?

• 25 hours
• 35 hours
• 45 hours
• 15 hours

Multiple Choice

Mrs. Collins made a scatterplot to show the relationship between the number of absences and a student’s final exam score. Based on this scatterplot, a student with 6 absences should get approximately what score on the final exam? 
Hint: create the trend line first

• 65
• 92
• 70
• 76

Multiple Choice

If Joe worked 30 hours, how much is he expected to earn?

• $600
• $200
• $1000
• $800

Multiple Choice

If Gold's Gym is looking to buy 30 TVs, how much will each one cost?

• 400
• 750
• 1250
• 0

Multiple Choice

If the carpenter worked for 6 days, how much did he earn?

• 1250
• 1500
• 1750
• 2000