Worksheet 3

Chapter 9: Correlation and Regression Section 9.1: Scatter Diagrams and Linear Correlation Name Date Objectives: • Make a scatter diagram. • Visually estimate the “best-fitting” line for a scatter diagram. • Use sample data to compute the sample correlation coefficient r . This worksheet will walk you through the steps to make a scatter diagram and visually estimate and draw the “best-fitting” line for the scatter diagram. You will then use the same sample data to compute the sample correlation coefficient r. The scatter diagram allows you to see whether there seems to be a linear relationship between x - and y - data pairs, and the “best-fitting” line shows you more precisely what that relationship might look like. The sample correlation coefficient r tells you how strong the relationship between the variables is. Instructions : Follow Steps 1–2 to make a scatter diagram and draw a “best-fitting” line for Exercise 14 in your textbook, which is reproduced below. Then use the sample data to compute the sample correlation coefficient r in Step 3. STEP 1: Make a scatter diagram. This will allow you to see, in general, whether there appears to be a linear relationship between the variables x and y and will give you the data points you need to construct a “best-fitting” line. Hannah Caple June 22 Downloaded by Jeremmy capilla (7pgdtdzn97@privaterelay.appleid.com) lOMoARcPSD|30869629

Chapter 9: Correlation and Regression Section 9.1: Scatter Diagrams and Linear Correlation Example: Make a scatter diagram of the data from Example 2 in the textbook, which is reproduced below. Since the x -values range from 70 to 125, use intervals of length 10 on the x -axis, with a jump from 0 to 70. Since the y -values range from 3 to 62, use intervals of length 10 on the y -axis, as well. Use intervals of length 10 on the y -axis. Use intervals of length 10 on the x -axis. Use a squiggle to show the jump, or change in scale, from 0 to 70. Label the diagram with a title and label the axes. Downloaded by Jeremmy capilla (7pgdtdzn97@privaterelay.appleid.com) lOMoARcPSD|30869629

Chapter 9: Correlation and Regression Section 9.1: Scatter Diagrams and Linear Correlation STEP 2: Draw a “best-fitting” line on the scatter diagram. This gives you a better visual of how good of a linear relationship there is between the variables. Example: Draw a “best-fitting” line through the data points on the scatter diagram from Example 2 from the textbook. Instructions: Draw a “best-fitting” line through the data points on the scatter diagram that you constructed in Step 1 for Exercise 14. The distance between the line and each data point should be as small as possible. Downloaded by Jeremmy capilla (7pgdtdzn97@privaterelay.appleid.com) lOMoARcPSD|30869629

Chapter 9: Correlation and Regression Section 9.1: Scatter Diagrams and Linear Correlation STEP 3: Compute the sample correlation coefficient, r . This coefficient helps you to assess the strength of the linear relationship between the two variables. Example: Compute the sample correlation coefficient r for the data from Example 2 in the textbook, which is reproduced again here: Downloaded by Jeremmy capilla (7pgdtdzn97@privaterelay.appleid.com) lOMoARcPSD|30869629

Chapter 9: Correlation and Regression Section 9.1: Scatter Diagrams and Linear Correlation Instructions: Compute the sample correlation coefficient r for the data in Exercise 14 in your textbook, which is reproduced on Page 1. n = Computation Table ( )( ) ( ) ( ) 2 2 2 2 2 2 7(18,458) (678)(166) 7(67,892) (678) 7(6768) (166) 0.949 n xy x y r n x x n y y - = - - - = - - » å å å å å å å x y 2 x 2 y xy x = å y = å 2 x = å 2 y = å xy = å ( )( ) ( ) ( ) 2 2 2 2 n xy x y r n x x n y y - = - - = å å å å å å å Note: If you enter the entire expression into your calculator at once, make sure to group the terms in the numerator, since they are being subtracted. In other words, enter the numerator expression into your calculator as (7(18,458) – (678)(166)). You should also group the radicals in the denominator inside parentheses, so that the calculator performs the multiplication before dividing. -0.9453 5 3 7 15 35 75 40 35 30 25 18 27 29.6 3488 293.2 -956 (3-27)2 (7-27)2 (15-27)2 (35-27)2 (75-27)2 (40-29.6)2 (35-29.6)2 (30-29.6)2 (25-29.6)2 (18-29.6)2 (3-27)2 x (40-29.6)2 (7-27)2 x (35-29.6)2 (15-27)2 x (30-29.6)2 (35-27)2 x (25-29.6)2 (75-2)2 x (18-29.6)2 Downloaded by Jeremmy capilla (7pgdtdzn97@privaterelay.appleid.com) lOMoARcPSD|30869629