ID - 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.

Time Studying (hours)

2

0.5

3

1

1.5

1

4

8

3

2.75

5

3

0

1.5

Score on Exam

87

72

92

86

89

76

99

94

96

90

92

87

67

74

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.

Score of final exam graph 

 

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

 

Correlation Practice

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

1. GraphOne.png

2. GraphTwo.png

3. GraphThree.png

4. GraphFour.png

5. GraphFive.png 

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

callout.png

Correlation and Causation

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 factors 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!

Correlation and Causation Practice

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

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

For each situation below, decide whether correlation implies causation. Did one of the variables CAUSE the other one to increase/decrease?

  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.

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

IMAGES CREATED BY GAVS