Scatter Plots and Linear Models

A scatter plot is a graph that is used to show data between two variables, also known as bivariate data.

• ​For ex: height and weight.​

​

Scatter plots show patterns, trends, and correlations between variables that could impact each other.​

Scatter Plots

​Positive Association	​Negative Association	​No Correlation
​Both variables are increasing.	One variable is increasing, the other is decreasing.​	There is no relationship between the variables.​

​Types of Correlation

Multiple Choice

What type of correlation does this graph have?

• positive 

• negative

• none

• all of the above

Multiple Choice

What is the correlation?

• Negative correlation

• No correlation

• Positive correlation

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

​

Match

Match the following

Non-linear Correlation

No Correlation

Positive, Linear Correlation

Negative, Linear Correlation

• Non-linear Correlation

• No Correlation

• Positive, Linear Correlation

• Negative, Linear Correlation

Multiple Choice

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

• Graph A

• Graph B

• Graph C

• Graph D

Correlation tests for a relationship between two variables. However, seeing two variables moving together does not necessarily mean we know whether one variable causes the other to occur. This is why we commonly say “correlation does not imply causation.”

Study Time and Grades

As study hours increase, grades increase. There is a positive correlation between hours and grades.

So....Do hours spent studying cause higher grades?

Ice Cream Sales and Shark Attacks

As ice cream sales increase, shark attacks increase. As ice cream sales decrease, shark attacks decrease.

So....ice cream sales cause shark attacks?

5G and COVID cases

There is a correlation between areas with 5G and high COVID cases.

So......Does 5G cause COVID?

Multiple Choice

This implies that one variable has a direct affect on the other variable.

• Correlation

• Causation

Multiple Choice

Correlation or Causation?

The number of times you come to tutoring and your test scores improving

• Correlation

• Causation

Multiple Choice

Correlation or Causation?

The inches of snowfall and the number of heart attacks

• Correlation

• Causation

​Outliers	​Clusters
​An outlier is a data point in a scatter plot that does not follow the trend of the data.	A group of data points that are closely grouped together.​

​outlier

cluster

Multiple Choice

What are the coordinates of the outlier?

• (1,9)

• (9,1)

• (2,2)

• y=x

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

​

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

Correlation coefficient (r) formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where:

• 1 indicates a strong positive relationship.

• -1 indicates a strong negative relationship.

• A result of zero indicates no relationship at all.

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = 1.2

• B) r = 0.89

• C)r = 0

• D) r = -0.89

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

Average time spent listening to music per day and average time spent watching TV per day.  $$r=-.17$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Score on science exam and number of words written on the essay question.  $$r=.28$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Number of steps taken per day and number of kilometers walked per day. $$r=.92$$  

• strong positive

• strong negative

• weak positive

• weak negative