1. Statistics: Scatter Plots and Lines of Fit

2. Vocabulary Scatter plot – Two sets of data plotted as ordered pairs in a coordinate plane Positive correlation – in a scatter plot, as x increases, y increases line of fit – a line that describes the trend of the data in a scatter plot Best-fit line – The line that most closely approximates the data in a scatter plot Negative correlation – in a scatter plot, as x increases, y decreases

3. y x y x x-y Coordinate Plane Quadrants III IIIIV Point Plotting (x, y) (-4, 7) (5, -8) x – left or right y – up or down right 5 down 8 left 4 up 7

4. Example 1a Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows average personal income for U.S. citizens. Answer:The graph shows a positive correlation. With each year, the average personal income rose.

5. Example 1b The graph shows the average students per computer in U.S. public schools. Answer: The graph shows a negative correlation. With each year, more computers are in the schools, making the students per computer rate smaller. Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.

6. Example 2a The table shows the world population growing at a rapid rate. YearPopulation (millions) 1650 500 18501000 19302000 19754000 19985900 Draw a scatter plot and determine what relationship exists, if any, in the data and draw a line of fit.

7. Example 2a cont Let the independent variable x be the year and let the dependent variable y be the population (in millions). The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables. Draw a line of fit for the scatter plot. No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot.

8. Example 2b Write the slope-intercept form of an equation for equation for the line of fit. The line of fit shown passes through the data points ( 1850, 1000 ) and ( 1998, 5900 ). Step 1Find the slope. Slope formula Let and Simplify.

9. Example 2b cont Step 2Use m = 33.1 and the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000). Slope-intercept form Answer:The equation of the line is.

10. Finding the Equation of Line of Best Fit Example 1: Find an equation for the trend line and the correlation coefficient. Fat(g) 671019202736 Calories 276260220388430550633 Calories and Fat in Selected Fast-Food Meals Solution: Use your graphing calculator to find the line of best fit and the correlation coefficient.

11. Cont (example 1)... Step 1. Use the EDIT feature of the STAT screen on your graphing calculator. Enter the data for fat (L 1 ) and the data for Calories (L 2 ) Fat(g) 671019202736 Calories 276260220388430550633 Calories and Fat in Selected Fast-Food Meals

12. Cont (example 1)... Step 2. Use the CALC feature in the STAT screen. Find the equation for the line of best fit  LinReg (ax + b) LinReg y = ax + b a = 13.60730858 b = 150.8694896 r 2 =.9438481593 r =.9715184812 Slope y-intercept Correlation coefficient The equation for the line of best fit is y = 13.61x + 150.87 and the correlation coefficient r is 0.9715184812

13. Finding the Equation of Line of Best Fit Example 2. Use a graphing calculator to find the equation of the line of best fit for the data at the right. What is the correlation coefficient? Estimate the recreation expenditures in 2010. YearDollars (Billions) 1993340 1994369 1995402 1996430 1997457 1998489 1999527 2000574 Recreation Expenditures Answers: y = 32.33x - 2671.67 r = 0.9964509708 The expenditures in 2010 will be 885 billions Let 1993 = 93

14. Example 3 Use the prediction equation y ≈ 33.1x – 60,235 where x is the year and y is the population (in millions), to predict the world population in 2010. Original equation Replace x with 2010. Simplify. Answer: 6,296,000,000