## Day 22 - Lesson 2.3

##### Learning Targets
• Estimate the correlation between two quantitative variables from a scatterplot.

• Interpret the correlation.

• Distinguish correlation from causation.

##### Activity:

We began this day by giving students examples of different distributions with their correlation.  We then used the Rossman/Chance applet to show randomly generated scatterplots. The class would call out guesses of what they thought the correlation was.  We did this three times as a class.  Make sure to show an example of a positive, negative and no direction.  On the activity page, the students sketched each scatterplot and described the distributions.   After going through the examples, we outlined our competition.  Each group of 4 would get one random distribution and would guess the correlation. The group closest to the correct correlation would win.  The applet can track performance so you don’t have worry about writing anything down, but be sure to keep an eye on which residual goes with each group.  Encourage the groups of 4 to reference and discuss the examples that had been given to make a better guess.  We suggest giving the groups up to 30 seconds to make their decision.  The other groups should also discuss quietly what their guess would be so they can get in some more practice.  The students had a lot of fun with this.  After each group had gone once they wanted to continue playing.  Most groups made pretty close guesses.  One group answered within 0.001 of the correct correlation!

##### Application 2.3: If I Eat Chocolate, Will I Win The Nobel Prize?

Students looked at the correlation between the number of Nobel prizes won by a country vs. the chocolate consumption of the country.  There is a fairly strong, positive, linear correlation between the variables.  This is an excellent example of why correlation does not equal causation since it would be absurd to think that chocolate would CAUSE a country to earn more Nobel prizes.

If there is time, check out some more ridiculous correlations at this website.