Scatter Plots And Line Of Best Fit Line Of Best

Scatter Plots and Line of Best Fit Line of Best Fit: Is the line that most closely follows a trend in data. The process of finding the best-fitting line to model a set of data is called linear regression. This process can be tedious to perform by hand, but you can use a graphing calculator to make a scatter plot and perform linear regression on a data set. EXAMPLE 1 The table below shows the total sales from women’s clothing stores in the United States from 1997 to 2002. Make a scatter plot of the data. Year Sales (billions of dollars)

1997 27.9

1998 28.7

1999 30.2

2000 32.5

2001 33.1

2002 34.3

Calculator Steps Step 1: Press the On button on the calculator. Step 2: Press the STAT and press 4 for ClrList press 2nd 1 , 2nd 2 press ENTER. Step 3: Press the STAT and press ENTER. Step 4: Enter years since 1997 since 1997 (0 ENTER, 1 ENTER, 2 ENTER, 3 ENTER, 4 ENTER, 5 ENTER) into List 1 (L1) These will be the x – values. Enter sales (in billions of dollars) into (L2). Press the key to get to (L2). These will be the y – values. Step 5: Press 2nd Y = then press ENTER. Make sure that Plot 1 is on and that the Xlist: L1 and the Ylist: L2. Step 6: Press Zoom 9 to display the scatter plot so that the points for all data pairs are visible. Step 7: Describe the correlation of the data in the scatter plot. ________________________ Step 8: Press STAT. From the CALC menu choose LinReg(ax + b). The a – and b – values given are for an equation of the form y = ax + b. Round these values to the nearest hundredth to write the equation: y = ax + b. Because r is close to 1, the data have a strong positive correlation. a = ____________, b = _________________, y = ax + b _____________________, r = _______________ Step 9: Press Y = and enter your equation from Step 8 for y1. Press Graph.

Graph what you see on the graph provided.

#1. Use the directions from the other page to complete this problem. The following table shows the total sales from men’s clothing stores in the United States from 1997 to 2002. Year Sales (billions of dollars)

1997 10.1

1998 10.6

1999 10.5

2000 10.8

2001 10.3

2002 9.9

1. Make a scatter plot of the data. Describe the correlation. (STEP 7)._______________________________

2. Find the equation of the best – fitting line for the data. (STEP 8) a = ________, b = _________, y = ax + b ______________, r = ___________________

3. Draw the best – fitting line for the data. (STEP 9)

4. What does the value of r for the equation tell you about the correlation of the data?

5. How could you use the best-fitting line to predict future sales of men’s clothing? Explain your answer.

6. Predict the sales from men’s clothing for the year 2007. Show your work.