1.5 Scatter Plots and Least Squares Lines Objective: To create a scatter plot and draw an informal...
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Transcript of 1.5 Scatter Plots and Least Squares Lines Objective: To create a scatter plot and draw an informal...
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
• Page 41• 13-20 all