Chapter 2 – Linear Equations and Functions 2.7 – Scatter Plots and Correlation

Chapter 2 – Linear Equations and Functions

2.7 – Scatter Plots and Correlation

2.7 – Scatter Plots and Correlation

• In this section we will review:– Correlations in scatter plots and

finding a best-fitting line

2.7 – Scatter Plots and Correlation

• Scatter plot – graph of a set of data pairs (x, y )

– Can help identify the relationship, or correlation, between two variables

2.7 – Scatter Plots and Correlation

• Positive correlation– As x increases, y increases.

2.7 – Scatter Plots and Correlation

• Negative correlation– As x increases, y decreases

2.7 – Scatter Plots and Correlation

• Relatively no correlation– There is no obvious pattern between

x and y

2.7 – Scatter Plots and Correlation

• Example 1– Describe the

correlation shown by the scatter plot.

2.7 – Scatter Plots and Correlation

• Example 2– Describe the

correlation shown in the scatter plot.

2.7 – Scatter Plots and Correlation

• Best-fitting line – the line that most closely models the data

– When points lie close, almost forming a line with positive or negative slope, the correlation is strong.

2.7 – Scatter Plots and Correlation

• Approximating a Best-Fitting Line1. Draw a scatter plot2. Sketch a line that follows the trend.

The line should be close to as many points as possible.

3. Choose two points that lie on the line and estimate the coordinates (they do NOT have to be original points)

4. Write an equation for the two points from step 3.

2.7 – Scatter Plots and Correlation

• Example 3– The table gives

the systolic blood pressure y of patients x years old. Approximate the best-fitting line for the data.

2.7 – Scatter Plots and Correlation

• Example 4– These data represent

purchases at five gas stations in a city.

– Approximate the best-fitting line.

– Predict the cost of 10 gallons of gasoline.

2.7 – Scatter Plots and Correlation

HOMEWORKWorksheet 2.7 Practice A