4.5 - Scatter Plots

​4.5 -

Scatter Plots​

Scatter Plots and Trend Lines​

Vocab

• Scatter plot: a graph with points plotted to show a relationship between 2 sets of data

• Correlations: describes relationships between 2 sets of data

• Positive Correlation: both data sets increase

• Negative Correlation: one set increases while the other decreases

• No Correlation: No relationship

• Trend Line (Line of best fit): Shows correlation between the data sets

​Example of a scatter plot

Bivariate data consist of two variables or two numerical observations. A scatter plot is a graph that shows the relationship between bivariate data. The data is graphed as ordered pairs on the coordinate plane. Once variable or value, does not necessarily depend on the other variable or value.

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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.

​Association/Pattern

To show the overall trend of a data set, we can use a ​Line of Best Fit.

​

A line of best fit should:

• Follow the trend of the data

• Split the data in half

• Help to estimate or predict values that are not already given in the set.

Line of Best Fit

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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 type of correlation does this scatter plot show?

• positive

• negative

• no correlation

• nonlinear association

Multiple Choice

What type of correlation does this graph have?

• positive

• negative

• none

• all of the above

Scatter Plots can be described as linear and non-linear models. They are not perfectly linear or non-linear but they​ follow a trend.

Linear vs. Non-linear Models

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Multiple Choice

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

• A
• B
• C
• D

Multiple Choice

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

• A
• B
• C
• D

Multiple Choice

What type of correlation is seen?

• strong positive

• strong negative

• weak positive

• none

Multiple Choice

What type of correlation (association) would you expect between the given variables?

The outside temperature and the amount of layers you wear. 

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

Multiple Choice

What type of correlation (association) would you expect between the given variables?

The number of siblings you have and your weight. 

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

​The numbers on the bottom of the next slide are the "correlation coefficients" -- pay close attention to them. How do they relate to the "slope" of the data?

Multiple Choice

Describe the following correlation coefficient.

$$r=-0.89$$  

• Strong positive 
• Weak positive 
• Strong negative 
• Weak negative 

Multiple Choice

If the correlation coefficient of a table of data is 0.85, what is true about the line of best fit?

• There is a weak, positive relationship
• There is a strong, positive relationship
• There is a weak, negative relationship
• There is a strong, negative relationship

Multiple Choice

Describe the following correlation coefficient.

$$r=-0.91$$  

• Strong positive

• Weak positive

• Strong negative

• Weak negative

Multiple Choice

Describe the correlation. r = 0.3

• Strong, positive

• Weak, positive

• Strong, negative

• Weak, negative

Multiple Choice

What is the correlation?

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

Multiple Choice

What kind of association does the scatter plot show?

• Positive

• Negative

• No association

Multiple Choice

What is the correlation?

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

Multiple Choice

Which scatter plot shows both positive and linear association?

Multiple Choice

What is a line of best fit used for?

• To make predictions
• To make the graph look pretty
• To connect the points
• To make it look like you know what you are doing