Scatter Plots & Trend Lines ext

Review:
Scatter Plots
& Trend Lines

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

Describe the correlation:

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

Multiple Choice

Describe the correlation:

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

Multiple Choice

Describe the correlation:

• 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

Drag and Drop

Choose the graph with a trend line that best fits the data.

Placeholder

Drag these tiles and drop them in the correct blank above

graph 1

graph 2

graph 3

graph 4

Multiple Choice

What is a line of best fit used for?

• To make predictions
• To make the graph look pretty
• To connect the points

Dropdown

Level 1: Determine the type of correlation.

Select answer

Drag and Drop

What is the type of correlation for the following scatter plot?

Placeholder

Drag these tiles and drop them in the correct blank above

Negative 

None

Positive 

Dropdown

What type of correlation does this scatter plot have?

Select answer

Drag and Drop

You are analyzing a scatter plot that has a negative correlation. What is true of the of the x and y values?

Placeholder

Drag these tiles and drop them in the correct blank above

As x increases, y decreases

As x increases, y increases

As x decreases, y decreases

Dropdown

As the age of the car increases, its value decreases. Which scatter plot represents this relationship?

Select answer

Dropdown

Which of the following lines represents the line of best fit for the scatter plot?

Select answer

Multiple Choice

Which sentence describes the relationship shown on this scatter plot?

• As the temperature decreases, the visitors increase. 
• As the temperature increases, the number of visitors increases. 
• As the visitors increase, the temperature decreases. 
• No correlation

Multiple Choice

the slope is -5/7, what does that mean?

• gain 5 hour of sleep for 7 cups of coffee
• lose 5 hours of sleep for 7 cups of coffee
• lose 7 cups of coffee for 5 hours of sleep
• lose 5 cups of coffee for 7 hours of sleep

Multiple Choice

The following scatter plot shows Pam's training as she prepares to run a 6 mile race at the end of the month.  Which of the following would be a reasonable approximation for the length of time it would take for her to run 6 miles? 

• A. 50 min
• B. 80 min
• C. 45 min
• D. 60 min

Multiple Choice

What type of association would you expect to see between the amount of fog in the sky and the distance that a pilot can see?

• Positive Association

• Negative Association

• No Association

• There is not enough information to tell.

Multiple Choice

Which scatter plot shows both positive and linear association?

Multiple Choice

What ordered pairs would you use to find the slope for the trend line?

• (1,0) (6,8)

• (8,6) (0,1)

Multiple Choice

What is the correlation?

• Negative correlation
• No correlation
• Positive correlation
• All of the above

Multiple Choice

Which sentence describes the relationship shown on this scatter plot?

• As the temperature decreases, the visitors increase. 
• As the temperature increases, the number of visitors increases. 
• As the visitors increase, the temperature decreases. 
• No correlation

Multiple Choice

What is a scatter plot?

• A graph that shows the relationship of two data sets.
• A graph drawn using rectangular bars to show how large each value is.
• A graph that shows information that is connected in some way.
• A graph that shows data changing over time.

Multiple Choice

You are analyzing a scatter plot that has a negative correlation. What is true of the of the x and y values?

• As x increases, y decreases
• As x increases, y increases
• As x decreases, y decreases

Multiple Choice

What type of correlation does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

Which scatter plot has the best trend line?

Multiple Choice

Julia created a scatter plot of the relationship between the number of fans at a school volleyball game, x, and the amount of money in dollars raised by selling concessions, y. She then drew the trend line and calculated the equation to be

y = 5.2x − 20.

Is the following statement TRUE or FALSE?

Concession sales will increase on average by $5.20 for each additional fan that attends the game.

• TRUE

• FALSE

• Not Enough Information

Multiple Choice

Julia created a scatter plot of the relationship between the number of fans at a school volleyball game, x, and the amount of money in dollars raised by selling concessions, y. She then drew the trend line and calculated the equation to be

y = 5.2x − 20.

Is the following statement TRUE or FALSE?

For every fan that attends the game, an average of $20 is raised by selling consessions.

• TRUE

• FALSE

• Not Enough Information

Multiple Choice

Julia created a scatter plot of the relationship between the number of fans at a school volleyball game, x, and the amount of money in dollars raised by selling concessions, y. She then drew the trend line and calculated the equation to be

y = 5.2x − 20.

Is the following statement TRUE or FALSE?

Julia can predict a loss of $20 if no fans attend a game.

• TRUE

• FALSE

• Not Enough Information

Multiple Choice

Julia created a scatter plot of the relationship between the number of fans at a school volleyball game, x, and the amount of money in dollars raised by selling concessions, y. She then drew the trend line and calculated the equation to be

y = 5.2x − 20.

Is the following statement TRUE or FALSE?

5.2 thousand fans attended the last game.

• TRUE

• FALSE

• Not Enough Information

Multiple Choice

Gabriella creates a scatter plot of the relationship between her hourly pay in dollars, y, and the number of coupon books she sells, x. She calculates the equation of the trend line to be y = 1.5x + 9.

What does the y-intercept represent?

• Gabriella earns $9 when 1 coupon book is sold

• Gabriella earns $9 when 0 coupon books are sold.

• Gabriella earns $1.50 per coupon book sold.

• Gabriella earns $9 per coupon book sold.

• Gabriella ears $9 by selling all her coupon books.

Multiple Select

Select ALL the terms that describe the association of the data graphed in the scatter plot.

• nonlinear

• linear

• negative

• positive

• no association

Multiple Choice

Are there any clusters in this scatter plot?

• No

• Yes, between 6 and 11 shots taken

• Yes, between 6 and 8 shots taken

• Yes, between 9 and 11 shots taken

Multiple Choice

Would you describe this association as strong or weak?

• Strong

• Weak

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 four additional players are added to the data set, which of the new points would be an outlier?

• (6, 2)

• (7, 3)

• (12, 11)

• (13, 6)

• None would be an outlier

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