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Splash Screen

Concept

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.

Regression Line INCOME The table shows the median income of U.S. families for the period 1970–2002. 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

Step 1 Make a scatter plot. STAT  EDIT Regression Line Step 1 Make a scatter plot. STAT  EDIT Enter the years in L1 and the income in L2. Step 2 Set the viewing window to fit the data. WINDOW  numbers will vary depending on problem Step 3 View the scatter plot. 2ND  Y= ENTER  SELECT “On”  GRAPH Step 4 Find the equation of the line of regression. STAT  > “CALC”  4 “LinReg(ax + b)”  ENTER TWICE Put information from a and b into the equation y = ax + b Example 2

WHAT YOU SHOULD SEE LinReg y=ax + b a=1349.867133 B=-2650768.344 Regression Line WHAT YOU SHOULD SEE LinReg y=ax + b a=1349.867133 B=-2650768.344 The regression equation is about y = 1349.87x – 2,650,768.34. The slope indicates that the income increases at a rate of about 1350 people per year. The correlation coefficient r is 0.997, which is very close to 1. So, the data fit the regression line very well. Example 2

Step 5 Graph the regression equation. Regression Line Step 5 Graph the regression equation. Copy the equation to the Y= list and graph. Y=  VARS  5 “Statistics”  >> “EQ”  ENTER Notice the equation is now in your Y= menu. GRAPH Notice that the regression line comes close to most of the data points. As the correlation coefficient indicated, the line fits the data well. Example 2

Step 6 Predict using the function. Find y when x = 2015. Regression Line Step 6 Predict using the function. Find y when x = 2015. 2ND  CALC  ENTER “value”  type in your x-value If your calculator gives you an error, you will need to reset the window size to accommodate your x-value. Answer: According to the function, the median income in 2015 will be about $69,220. Example 2

The table shows the winning times for an annual dirt bike race for the period 2000–2008. Use a graphing calculator to make a scatter plot of the data. Find and graph a line of regression. Then use the function to predict the winning time in 2015. A. y = –15.75x + 31,890.25; about 154 seconds B. y = –14.75x + 29,825.67; about 104 seconds C. y = –14.6x + 29,604.72; about 186 seconds D. y = –14.95x + 30,233.25; about 99 seconds Example 2

Additional Example 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 how years of experience are related to hourly rate of pay. b. Write an equation to show how 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.