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Recognizing Differences in Scatter Plots

3.4.2 Recognizing Differences in Scatter Plots

3.4.2 • Recognizing Differences in Scatter Plots

Activity

Your teacher will give you a set of cards that show scatter plots of data. Sort the cards into 2 categories of your choosing. Be prepared to explain the meaning of your categories. Then, sort the cards into 2 categories in a different way. Be prepared to explain the meaning of your new categories.

Compare your answer:

Your answer may vary, but here are some samples.

  • Scatter plots that look linear: C, D, F, G. Scatter plots that are not very linear: A, B, E, H, I, J
  • Generally increasing: E, F, G, I. Generally decreasing: A, C, D, J. Not really increasing or decreasing: B, H

Self Check

Which correlation coefficient best matches the scatter plot below?

 

  1. r = − 0.39
  2. r = 0.26
  3. r = − 0.89
  4. r = 0.95

Additional Resources

Correlation Coefficient

The correlation coefficient is a number between −1−1 and +1+1 (including −1−1 and +1+1) that measures the strength and direction of a linear relationship. The correlation coefficient is denoted by the letter rr. Several scatter plots are shown below. The value of the correlation coefficient for the data displayed in each plot is also given.

Scatter plot showing a perfect positive linear relationship between x and T values. The graph is labeled with r equal to 1.00. As x increases, y also increases. Scatter plot showing a positive linear relationship between x and T values. The graph is labeled with r equal to 0.71, indicating a moderate relationship. Scatter plot showing a relationship between x and T values. The graph is labeled with r equal to 0.32 which indicates a weak relationship because the points are scattered and do not form a clear linear pattern. Scatter plot showing the relationship between x and T values. The graph is labeled with r equal to negative 0.10 which indicates a very weak relationship because the data points are widely spread and do not show a clear trend. Scatter plot with points scattered across the graph, showing a weak negative correlation between x and T values. The correlation coefficient, r equal to negative 0.32, is displayed at the top. Scatter plot showing a negative linear relationship between x and T values. The graph is labeled with r equal to negative 0.63, indicating a moderate relationship. Scatter plot showing a perfect negative linear relationship between x and T values. The graph is labeled with r equal to negative 1.00. As x increases, y decreases.

When is the value of the correlation coefficient positive?

  • The correlation coefficient is positive when as the xx-values increase, the yy-values also tend to increase.

When is the value of the correlation coefficient negative?

  • The correlation coefficient is negative when as the xx-values increase, the yy-values tend to decrease.

Is the linear relationship stronger when the correlation coefficient is closer to 0 or to 1 (or −1−1)?

  • As the points form a stronger negative or positive linear relationship, the correlation coefficient gets farther from 0. Students note that when all of the points are on a line with a positive slope, the correlation coefficient is +1+1. The correlation coefficient is −1−1 if all of the points are on a line with a negative slope.

The table below shows how you can informally interpret the value of a correlation coefficient.

If the value of the correlation coefficient is . . . You can say that . . .
r=1.0r=1.0 There is a perfect positive linear relationship.
0.7≤r<1.00.7≤r<1.0 There is a strong positive linear relationship.
0.3≤r<0.70.3≤r<0.7 There is a moderate positive linear relationship.
0<r<0.30<r<0.3 There is a weak positive linear relationship.
r=0r=0 There is no linear relationship.
−0.3<r<0−0.3<r<0 There is a weak negative linear relationship.
−0.7<r≤−0.3−0.7<r≤−0.3 There is a moderate negative linear relationship.
−1.0<r≤−0.7−1.0<r≤−0.7 There is a strong negative linear relationship.
r=−1.0r=−1.0 There is a perfect negative linear relationship.

Try it

Correlation Coefficient

Which of the three scatter plots below shows the strongest linear relationship? Which shows the weakest linear relationship? Explain your answers.

Three scatter plots, each with different data distributions.

Compare your answer:

Your answer may vary, but here is a sample.

The strongest linear relationship would be Scatter Plot 3. The points are closest to having a linear model. The weakest linear relationship would be Scatter Plot 2 because the points are spread apart the most and are less likely to have a strong linear relationship.