Embedded Files
Introduction
Introduction
In this lesson you will:
practise making predictions with data
explore lines of best fit
learn about and practise interpreting the correlation coefficient.
Activity 1 - Making predictions
Activity 1 - Making predictions
Use the Desmos activity, Making predictions in a scatter plot, to practise making predictions with data.
Open the Desmos interactive in a new tab by clicking on the image below. If the folder tab is open on the left hand side of the screen close it so you can see the graph in full screen.
Complete this activity by exploring each example in turn. (Use the green slider at the bottom of the screen to move through the different examples.)
Activity 2 - Fitting a line of best fit by eye
Activity 2 - Fitting a line of best fit by eye
A line of best fit on a graph shows the general direction that a group of points seems to follow.
We can use the line to interpolate or extrapolate data.
Interpolation
Interpolation
Interpolation is where we find a value inside our set of data points.
Here we have used interpolation to estimate the sales at 21 oC.
Extrapolation
Extrapolation
Extrapolation is where we find a value outside our set of data points.
Here we have used extrapolation to estimate the sales at 29 oC.
Note: This estimate is higher than any value we had. We must be careful with extrapolation as we can only guess that the data will continue to follow the same trend.
Task 1 - Understanding the line of best fit
Task 1 - Understanding the line of best fit
Consolidate your understanding by watching Eddie Woo explain how to find a line of best fit by eye.
Line of Best Fit (1 of 2: Overview)
Duration: 12:18
Task 2 - Applying your understanding
Task 2 - Applying your understanding
Use the following Desmos interactives to practise finding a line of best fit.
Note: To use the the interactives you need to open each link in a new tab by clicking on the image. If the folder tab is open on the left hand side of the screen close it so you can see the graph in full screen.
Correlation 1: Minimising the distance of the points from the line
Correlation 2: Practising minimising the distance of the points from the line
Activity 3 - Interpreting the correlation coefficient
Activity 3 - Interpreting the correlation coefficient
What is the correlation co-efficient?
What is the correlation co-efficient?
The word correlation is made up of ‘co’ meaning together and ‘relation.’
When two sets of data are strongly linked together we say they have a high correlation.
Correlation is positive when the values increase together.
Correlation is negative when one value decreases as the other increases.
A correlation is assumed to be linear (a straight line).
We assign numbers or a correlation coefficient to describe how strong the relationship is between the two variables. (In other words, how close to a straight line the data is.)
1 is a perfect positive correlation.
0 is no correlation – there seems to be no relationship at all.
-1 is a perfect negative correlation.
Compare these two graphs
Compare these two graphs
In both of these cases there is no relationship.
There is no dependent variable.
One variable is changing regardless of what happens with the other variable.
Task 1 - Creating data sets
Task 1 - Creating data sets
Open the Desmos interactive, Investigating the correlation co-efficient in a new tab by clicking on the image. (If the folder tab is open on the left hand side of the screen close it so you can see the graph in full screen.)
Complete this activity by moving the green dots to create datasets that have a correlation of 1, -1 and 0.
Task 2 - Practise guessing the correlation
Task 2 - Practise guessing the correlation
Open the Geogebra interactive, Guess the correlation in a new tab by clicking on the image.
Start the activity by clicking the new sample button.
Type in your guess then check how clsoe you were.
Optional activity - Finding equation for a line of best fit
Optional activity - Finding equation for a line of best fit
To find an equation for a line of best fit, we will use the general equation of a line:
Use this example to complete the activity below:
Activities too hard?
Activities too hard?
Visit the Plotting scatter graphs activity on the Transum website to practise plotting scatter graphs from data representing a number of different everyday situations.
Visit the Deconstructing graphs activity on the Transum website to practise filling in the tables of values from the information that can be read from the given graphs.
Activities too easy?
Activities too easy?
Complete the Scatter plots 1 activity on the Open Middle website.
Complete the Scatter plots 2 activity on the Open Middle website.
Watch the video Line of best fit with your calculator - CASIO on YouTube.
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
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