1.5 Scatter Plots and Least Squares Lines Objective: To create a scatter plot and draw an informal inference; use your calculator to find the equation.

1.5 Scatter Plots and Least Squares Lines

Objective: To create a scatter plot and draw an informal inference; use your

calculator to find the equation for the least squares line.

Scatter Plots

Scatter Plots

• In many real-world problems, you will find data that relate two variables such as time and distance or age and height. You can view the relationship between two variables with a scatter plot.

Scatter Plots

• The following data on the number of reported cases of chicken pox in thousands in the United States is graphed in a scatter plot. The variable x represents the number years after 1988 (x = 0 is 1988) and y represents the number of cases in thousands.

Scatter Plots

• The chicken pox data involves a two-variable data set that has a negative correlation. In general, there is a correlation between two variables when there appears to be a line about which the data points cluster. There are three situations:

Scatter Plots

• A scatter plot can help you see patterns in data involving two variables. If you think there may be a linear correlation between the variables, you can use a calculator to find a linear-regression line, also called the least-squares line, that best fits the data.

Scatter Plots

• The graph below shows the vertical distance from each point in a scatter plot to a fitted line. The fit of a least-squares line is based on minimizing these vertical distances for a data set. A least-squares line is one type of linear model for a data set.

Example 1

Scatter Plots

• First, hit the stat button. This screen should appear.

Scatter Plots

• First, hit the stat button. This screen should appear.• Now, hit enter to choose edit. This screen should

appear.

Scatter Plots

• First, hit the stat button. This screen should appear.• Now, hit enter to choose edit. This screen should

appear.• Now, enter you values for x under L1. After you enter

each value, hit enter.

Scatter Plots

• Select the right arrow key to move to L2. Enter your y values there. Hit enter after each value.

Scatter Plots

• Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear.

Scatter Plots

• Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear.

• Now hit enter and this screen should appear.

Scatter Plots

• Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear.

• Now hit enter and this screen should appear.• Hit enter again to select on.

Scatter Plots

• Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear.

• Now hit enter and this screen should appear.• Hit enter again to select on. • Hit graph to see the scatter plot.

Scatter Plots

• Now, select stat plot by selecting the blue 2nd key and the y = key. This should appear.

• Now hit enter and this screen should appear.• Hit enter again to select on. • Hit graph to see the scatter plot.• Adjust your window to see all values.

Example 1

Scatter Plots

• Now, select the stat key. Next select CALC. • Now, select LinReg(ax+b). Hit enter twice.

Scatter Plots

• Now, go to y= and enter the equation of the least-squares line.

Example 1

Correlation and Prediction

Correlation and Prediction

Example 2

Example 2

Homework

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