Scatter Plots and Linear Regression 2 5 Correlations

Scatter Plots and Linear Regression 2. 5

Correlations

• When you find a line that closely approximates a set of data, you are finding a line of fit for the data. • An equation of such a line is often called a prediction equation because it can be used to predict one of the variables given the other variable.

Example 1 • a) Use the data to make a scatter plot to find a correlation between the points. • b) Use a graphing calculator to find an equation for the line of regression.

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Example 2 INCOME The table shows the median income of U. S. families for the period 1970– 2002. Data for L 1 should be years since 1970. Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the median income in 2015.

Example 2 WHAT YOU SHOULD SEE Lin. Reg y=ax + b a= 1349. 867133 b = 8469. 907343 The regression equation is about y = 1349. 867 x + 8469. 907. The slope indicates that the income increases at a rate of about $1350 per year.

Example 2 Then use the equation to predict the median income in 2015. Answer: According to the function, the median income in 2015 will be about $69, 213. 92.

Example 3 The table below shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each technician earns. Experience (years) 9 4 3 1 10 6 12 8 Hourly Rate of Pay $17 $10 $7 $19 $12 $20 $15 a. Draw a scatter plot to show years of experience are related to hourly rate of pay. b. Write an equation to show years of experience (x) are related to hourly rate of pay (y). c. Use the function to predict the hourly rate of pay for 21 years of experience.