IRTVD - Scatter Plots and Correlation (Lesson)

Scatter Plots and Correlation

When given two real-world variables such as height and weight, you get a set of bivariate data that can be plotted on a coordinate plane. Let's try an example.

After the final exam, Mrs. Smith asked her students to estimate how many hours they spent studying. Below is a table giving the amount of time each student studied along with their score on the test.

First, let us identify the independent variable, this is usually the variable that can be controlled and in this case, it would be the time spent studying. The dependent variable is the score on the exam or the variable that is going to be affected. When constructing a scatter plot, we will put the independent variable on the x-axis and the dependent variable on the y-axis.

When given a scatter plot, one of the first values we want to identify is the correlation coefficient .

For each scatter plot below, chose the type of correlation and estimate the correlation coefficient (r).

1.

2.

3.

4.

5.  

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In the example about Mrs. Smith's test scores, you would expect that the amount of time a student spent studying has an effect on their final exam score. While it does, there are other factor's that contribute to the student's score, such as how much they retained throughout the semester or even how much sleep they got the night before.

At times, students make an error when interpreting correlation and causation. Just because a correlation exists between two variables, that does not mean that one variable causes the other.

Correlation does not imply causation!

For each situation below, state whether you would expect to see a positive correlation, negative correlation or no correlation.

1. Hours spent practicing free throws and number of free throws made in the game.
2. Number of computers a school has and number of baseball games they win.
3. The amount of miles driven and the amount of gas in your tank.
4. Pollution levels of a city & the amount of registered cars in the city.
5. The $ amount you can ask for a car & the # of miles on the odometer

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For each situation below, decide whether correlation implies causation.

1. Researchers noticed that as ice cream sales go up, shark attacks go up
2. The longer you exercise, the more calories you burn
3. Surveys show workers who are happier at their jobs are more productive
4. The more you drive, the less gas you have in your tank
5. The longer you study, the higher your grade is
6. The bigger a room is, the longer it takes to paint

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IMAGES CREATED BY GAVS