​Types of Association

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

​

​outlier

cluster

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

​

Reminders

Types of association

​Negative Correlation

​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.

​

​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

​

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

​

​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?

Scatter Diagrams and Correlation

Learning Objectives

• Able to understand bivariate data

• Able to draw scatter diagram

• Able to identify whether or not there is a positive or a negative correlation between the two variables

• Able to draw lines of best fit

Introduction

• Bivariate data is data for two variables (usually two types of related data).

• A scatter plot (or scatter diagram or scatter graph) explores the relationship between two sets of data.

• Plotting each pair of numbers as a dot allows you to see whether a general pattern emerges.

Example 1

Ice cream sales versus the temperature on that day. The two variables are Ice Cream Sales and Temperature.

Positive correlation

Having both sets of data going up together is called a positive relationship (or positive correlation).

Negative correlation

When one set of data goes up as the other goes down, you have a negative relationship (or negative correlation).

No correlation

Randomly scattered dots show that there is no relationship between the two sets of data.

Lines of best fit

• When points on a scatter plot show a linear correlation, you can use a line to model the data.

• This line is called the line of best fit or trend line and is drawn through the data so that there are an equal number of points above and below it.

Non-linear relationship

Other data may be better matched with a non-linear relationship, such as a parabolic or a logarithmic curve.

Interpolation and extrapolation

Lines of best fit are used to estimate what might happen between known data values (interpolation) and to predict what might happen beyond known data values (extrapolation).

Draw the line by eye

• Ensure that there are an equal number of points above and below the line.

• Attempt to position the line so the average distance from the line to points above is the same as the average distance to the points below.

The equation of the line

• The general equation of a straight line linking the variables x and y is:  y = mx + b

  where m is gradient of the line and b is y-intercept.