Scatter Plots and Correlations

Is there a relationship between the amount of gas put in a car and the number of miles that can be driven?

Positive Correlation

As one set of data values increases, so does the other.

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Positive Correlation

Is there a relationship between the number of things you buy at the mall and the amount of money you have left?

Negative Correlation

As one set of data values increases, the other decreases.

Negative Correlation

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Is there a relationship between a person’s age and the temperature outside?

No Correlation

There is no relationship between the two sets of data.

No Correlation

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Would a scatter plot show a positive,negative, or no

correlation?Number of pages printed by a printer and the amount of ink left in the cartridge.– Negative Correlation!

Would a scatter plot show a positive,negative, or no

correlation?

Age of a child and the child’s shoe size– Positive Correlation!

Would a scatter plot show a positive,negative, or no

correlation?Number of letters in a person’s first name and the person’s height.– No Correlation!

Would a scatter plot show a positive,negative, or no

correlation?

Shots attempted and the number of points made in a basketball game– Positive Correlation!

Would a scatter plot show a positive,negative, or no

correlation?

Length of a taxi ride and the amount of the fare– Positive Correlation!

Would a scatter plot show a positive,negative, or no

correlation?

Outside temperature and the cost of air conditioning.– Positive Correlation!

Would a scatter plot show a positive,negative, or no

correlation?

Miles ridden on a bicycle and the thickness of the tire tread– Negative Correlation!

Would a scatter plot show a positive,negative, or no

correlation?

Temperature outside and the amount of clothing a person wears– Negative Correlation!

Think of some situations that show a….

Positive Correlation:

Negative Correlation:

No Correlation:

Which graph to use…..?

Use bar graphs to make comparisons.Use line graphs to show change over time.Use circle graphs to show percentage of a whole.Use histograms when the data is arranged in intervals.Use scatter plots to show correlations between two sets of numerical data.

Correlation Coefficient

Scatterplot displays the strength, direction, and form of the relationship between two quantitative variables.A correlation coefficient measures the strength of that relationship.

Correlation Coefficient Strength

Go to stat key and choose 1 Edit. Enter the data into lists L1 and L2 on a graphing calculator. To clear an existing list arrow up to L1 and press clear and arrow down. The list will be cleared. Use the linear regression feature by pressing STAT, choosing CALC, and selecting 4:LinReg. The equation of the line of best fit will appear.

Example 2: Anthropology Application

Anthropologists can use the femur, or thighbone, to estimate the height of a human being. The table shows the results of a randomly selected sample.

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•a. Make a scatter plot of the data with femur length as the independent variable.The scatter plot is shown at right.

Example 2 Continued

b. Find the correlation coefficient r and the line of best fit. Interpret the slope of the line of best fit in the context of the problem. Enter the data into lists L1 and L2 on a graphing calculator. Use the linear regression feature by pressing STAT, choosing CALC, and selecting 4:LinReg. The equation of the line of best fit is h ≈ 2.91l + 54.04.

Example 2 Continued

The slope is about 2.91, so for each 1 cm increase in femur length, the predicted increase in a human being’s height is 2.91 cm.

The correlation coefficient is r ≈ 0.986 which indicates a strong positive correlation.

Example 2 Continued

c. A man’s femur is 41 cm long. Predict the man’s height.

Substitute 41 for l.

The height of a man with a 41-cm-long femur would be about 173 cm.

h ≈ 2.91(41) + 54.04

The equation of the line of best fit is h ≈ 2.91l + 54.04. Use the equation to predict the man’s height. For a 41-cm-long femur,

h ≈ 173.35

Example 2 Continued