Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Scatter Plots: Review & New Terms

We have examined relationships between sets of ordered pairs or data. Displaying data visually can help you see relationships.

A scatter plot is a graph with points plotted to show a possible relationship between two sets of data.

Let’s look at some examples . . .

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Example 1: Graphing a Scatter Plot from Given DataThe table shows the number of cookies in a jar from the time since they were baked. Graph a scatter plot using the given data.

Use the table to make ordered pairs for the scatter plot.

The x-value represents the time since the cookies were baked and the y-value represents the number of cookies left in the jar.

Plot the ordered pairs.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

The table shows the number of points scored by a high school football team in the first four games of a season. Graph a scatter plot using the given data.

Use the table to make ordered pairs for the scatter plot.

The x-value represents the individual games and the y-value represents the points scored in each game.

Plot the ordered pairs.

Game 1 2 3 4

Score 6 21 46 34

Example 2: Graphing a Scatter Plot from Given Data

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Scatter Plots can be described using a variety of terms.

1.) Positive Correlation/Negative Correlation/ No Correlation.

A correlation describes a relationship between two data sets. A graph may show the correlation between data. The correlation can help you analyze trends and make predictions. There are three types of correlations between data.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Increasing can also be used to describe this graph.

Decreasing can also be used to describe this graph.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

2.) Linear Association/Non-Linear Association: A relationship that can be represented by a straight line has a linear association.

A relationship which cannot be represented by a straight line has a non-linear association.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

3.) Outlier: An element of a data set that distinctly stands out from the rest of the data.

4.) Clustering: The partitioning (dividing) of a data set into subsets (clusters), so that the data in each subset (ideally) share some common trait (the tighter the cluster, the stronger the relationship between the 2 variables).

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

5.) Greatest Rate of Change/Least Rate of Change

Remember that the rate of change is the ratio of the change in the output (y) value over the input value (x) (slope). Slope is a measure of steepness of a line.

Therefore:• the greater the rate of change, the steeper the slope, and the higher the value of m (m = 5).

• the lower the rate of change, the flatter the slope, and the lower the value of m (m = 1/5).

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Whiteboard Practice

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Using the descriptions that can be applied scatter plots, describe the graph.

Positive correlation; linear association.

As the average daily temperature increased, the number of visitor increased.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Negative correlation, linear association.

As the years passed, the amount of the car property tax bill decreased.

Using the descriptions that can be applied scatter plots, describe the graph.

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Car Property Tax

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Positive correlation, linear association.

As the years passed, the number of participants in the snowboarding competition increased.

Using the descriptions that can be applied scatter plots, describe the graph.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Positive correlation, linear association.

As the years passed, the number of participants in the snowboarding competition increased.

Using the descriptions that can be applied scatter plots, describe the graph.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Using the descriptions that can be applied scatter plots, describe the graph.

No correlation, non-linear association. Temperature

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Holt Algebra 1

4-5 Scatter Plots and Trend Lines

the number of people in an audience and ticket sales

You would expect to see a positive correlation. As the number of people in the audience increases, ticket sales increase. Linear association.

Example 2: Identifying Correlations Identify the correlation you would expect to see between the pair of data sets. Explain. What other descriptions could be used?

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

a runner’s time and the distance to the finish line

You would expect to see a negative correlation. As a runner’s time increases, the distance to the finish line decreases. Linear association.

Example 3: Identifying Correlations

Identify the correlation you would expect to see between the pair of data sets. Explain.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Identify the type of correlation you would expect to see between the pair of data sets. Explain.

the temperature in Houston and the number of cars sold in Boston

You would except to see no correlation. The temperature in Houston has nothing to do with the number of cars sold in Boston. Non-linear association.

Example 4: Identifying Correlations

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

the number of members in a family and the size of the family’s grocery bill

You would expect to see positive correlation. As the number of members in a family increases, the size of the grocery bill increases. Linear association.

Identify the type of correlation you would expect to see between the pair of data sets. Explain.

Example 5: Identifying Correlations

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

the number of times you sharpen your pencil and the length of your pencil

You would expect to see a negative correlation. As the number of times you sharpen your pencil increases, the length of your pencil decreases. Linear association.

Identify the type of correlation you would expect to see between the pair of data sets. Explain.

Example 6: Identifying Correlations

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Example 1: Matching Scatter Plots to Situations

Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.

Graph A Graph B Graph C

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Example 4 ContinuedChoose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.

Graph A

The age of the car cannot be negative.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Example 4 Continued

Graph B

This graph shows all positive values and a positive correlation, so it could represent the data set.

Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Example 4 Continued

Graph C

There will be a positive correlation between the amount spent on repairs and the age of the car.

Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Graph A Graph B Graph C

Example 4 Continued

Graph A shows negative values, so it is incorrect. Graph C shows negative correlation, so it is incorrect. Graph B is the correct scatter plot.

Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Check It Out! Example 4

Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain.

Graph A Graph B Graph C

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Check It Out! Example 4 Continued

Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain.

Graph A

The pie is cooling steadily after it is take from the oven.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain.

Graph B

The pie has started cooling before it is taken from the oven.

Check It Out! Example 4 Continued

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Check It Out! Example 4 Continued

Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain.

Graph C

The temperature of the pie is increasing after it is taken from the oven.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Check It Out! Example 4

Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain.

Graph A Graph B Graph CGraph B shows the pie cooling while it is in the oven, so it is incorrect. Graph C shows the temperature of the pie increasing, so it is incorrect. Graph A is the correct answer.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Which scatter plot shows the greatest rate of change? Which shows outliers? Explain.

The graph on the left shows the greatest rate of change. It also shows an outlier.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Which scatter plot shows the least rate of change? Which shows outliers? Explain.

The graph on the right shows the least rate of change. Both graphs show outliers.

Holt Algebra 1

4-5 Scatter Plots and Trend Lines

Which scatter plot shows the greatest rate of change? Which shows more clustering? Explain.

The graph on the left shows the greatest rate of change. It also shows more potential clusters.