Line of best fit - Scatter Plots

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 associations between variables that could impact each other.​

Scatter Plots

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

​Types of Association

Multiple Choice

What type of association 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

​

Multiple Choice

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

• Graph A

• Graph B

• Graph C

• Graph D

​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

Multiple Choice

Determine the correlation.

• positive

• negative

• no correlation

Multiple Choice

Determine the correlation.

• positive

• negative

• no correlation

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

Drag and Drop

Based on the Desmos shown, what is the equation for the line of best fit?

y = ​

Placeholder

x + ​

Placeholder

Drag these tiles and drop them in the correct blank above

1.14662

0.562221

0.8911

5.06

7.23

0.7941

Drag and Drop

The data in the graph shown represents your grade point average (GPA) based on how many semesters you've been in high school. X represents the number of semesters completed, y represents your GPA. Isaac wants to use this to predict his GPA at the end of his freshman year (2 semesters)

Fill in the blanks based on what he would need to type into a calculator to make this prediction:

​

Placeholder

* ​

Placeholder

+ ​

Placeholder

Drag these tiles and drop them in the correct blank above

1.14662

2

0.562221

0.8911

5.06

7.23

0.7941

4

Reminders

Types of association

​Negative Correlation

Multiple Choice

Describe the correlation in the graph shown.

• Strong Negative

• Strong Positive

• Weak Negative

• Weak Positive

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

Describe a correlation with a coefficient of r=0.3

• Strong positive

• Weak positive

• Strong negative

• Weak negative

Multiple Choice

About how many points would we expect if Vasu played 40 minutes?

• 10

• 24

• 28

• 32

Poll

How well do you understand scatter plots?

• Thumbs up! (I got it)

• Thumbs Sideways(Im getting it)

• Thumbs down(why do we keep learning japanese in math?)