1. Aim: How can we use trend lines to make predictions and understand correlation?
Problem of the Day:

2. Aim: How can we use trend lines to make predictions and understand correlation?
Problem of the Day:
The chart below shows how many people downloaded an album each day after it was released. On the grid below, draw a scatter plot of this information.

3. Aim: How can we use trend lines to make predictions and understand correlation?
Motivation:
Using your scatter plot can predict how many times the album will be downloaded on the 9th day?

4. Aim: How can we use trend lines to make predictions and understand correlation?
A trend line is a line drawn on a scatter plot near the points. It shows a correlation.

5. Aim: How can we use trend lines to make predictions and understand correlation?
The trend line we will use in this class is the line of best fit.
Line of best fit (def.) The most accurate line on a scatter plot showing the relationship between bivariate data.

6. Trend Lines & Predictions
Aim: How can we use trend lines to make predictions and understand correlation?
Trend Lines & Predictions
As mentioned earlier, we can use trend lines to help us make predictions. In math, when you predict or estimate a value beyond what we already know, we call this process extrapolation.

7. Trend Lines & Predictions
Aim: How can we use trend lines to make predictions and understand correlation?
Trend Lines & Predictions
However, when we predict or estimate between values we already know, we call this process interpolation.

8. a. Predict the wingspan of a hawk that is 22 in. long.
Aim: How can we use trend lines to make predictions and understand correlation?
Example #1:
Given the scatter plot and line of best fit comparing the length and wingspan of hawks, answer the following?
a. Predict the wingspan of a hawk that is 22 in. long.
b. Is this prediction extrapolation or interpolation? Why?

9. Aim: How can we use trend lines to make predictions and understand correlation?
So far we have studied that two quantities could have a relationship between them if we notice certain trends in a scatter plot of their data. However, it is also important to know that because two quantities are related does not automatically mean that they share a "cause and effect" relationship.

10. Aim: How can we use trend lines to make predictions and understand correlation?
There is a positive correlation between the number of TV's you have and the average life expectancy of the family members. However we all know that owning more TV's does not allow you to live a longer life! So what is going on here?

11. "CORRELATION IS NOT THE SAME AS CAUSATION!"
Aim: How can we use trend lines to make predictions and understand correlation?
Owning more TV's means that you have more money, which means that you should have more money to spend on healthcare.
In mathematics we refer to these type of situations by saying:
"CORRELATION IS NOT THE SAME AS CAUSATION!"

12. Causation vs. Correlation:
Aim: How can we use trend lines to make predictions and understand correlation?
Causation vs. Correlation:
Causation occurs when a change in one quantity produces a change in another quantity.

13. Aim: How can we use trend lines to make predictions and understand correlation?
Example #2:
Determine whether the following examples that have a correlation also have causation.
1. Children with bigger feet spell better.
Children with bigger feet spell better because they're older, their greater age bringing about bigger feet and, not quite so certainly, better spelling.
2. People who smoke develop lung cancer.
It has been clinically proven that an individual’s smoking behavior can cause them to develop lung cancer.
3. Height of a plant increases as the amount of sunlight it receives increases.
There is both causation and correlation.

14. Aim: How can we use trend lines to make predictions and understand correlation?

15. Aim: How can we use trend lines to make predictions and understand correlation?

16. Homework# pg 49 #'s 31 a-b, 32, 35 pg 50 #'s 13,14,18
Aim: How can we use trend lines to make predictions and understand correlation?
Homework#
pg 49 #'s 31 a-b, 32, 35
pg 50 #'s 13,14,18

17. Aim: How can we use trend lines to make predictions and understand correlation?

18. Attachments