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 Line Draw a scatter plot Sketch a line that follows the trend. The line should be close to as many points as possible. Choose two points that lie on the line and estimate the coordinates (they do NOT have to be original points) 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 HOMEWORK Worksheet 2.7 Practice A