Correlation
Advice
Applets
- Guessing Correlations
- A great "game" with four plots that appear and the correlation is to be guessed (multiple choice). No special prep is required to use.
- Can choose the number of data points, change the data values, and view graphs of guess vs. actual, error vs. actual, and error vs. trial.
Fun Stuff
- I like this comic for a rejoinder to the correlation does not equal causation discussion. xkcd comic
- Global Average Temperature vs. Number of Pirates
Sample activity or homework assignment
Correlation between
mileage and greenhouse gas emissions
The EPA/DOE site http://www.fueleconomy.gov/ provides consumers information on cars relating to size, miles per gallon (mpg), and emissions.
Click on “Find and Compare” and select the model year 2009, a manufacturer and model.
- For at least 12 different cars, record their highway miles per gallon (use the official EPA MPG) and Carbon Footprint (tons/yr of greenhouse gas emissions). I recommend you use a variety of different types of cars for best results. DO NOT INCLUDE HYBRIDS!
Example:
- Plot the 12 points with mpg on the horizontal axis and emissions on the vertical axis. Describe the correlation between the two variables.
- Find the correlation coefficient r. Is its value consistent with the scatterplot you drew from #2?
- Find the least squares line and draw it on your scatter plot. Be sure to plot the point
.
- What is the slope of the least squares line? What is the interpretation of the slope in this scatter plot?
- The Honda Civic Hybrid gets 45 mpg on the highway. Using your least squares line, predict the greenhouse gas emissions of this car. Does your answer make sense? Why or why not?