Statistics: Scatter Plots and Lines of Fit

Transcription

1 Statistics: Scatter Plots and Lines of Fit This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are included under the Fair Use exemption of the U. S. Copyright Law. Further use of these materials and this presentation is restricted.

2 Objectives Students will interpret points on a scatter plot. Students will write equations for lines of fit. 2

3 Vocabulary scatter plot a graph in which two sets of data are plotted as ordered pairs. positive correlation x increases as y increases. negative correlation as x increases, y decreases. line of fit the line that describes the trend of the data best-fit line a statistical method that most closely approximates the data linear interpolation predict values that are inside the range of the data. 3

4 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. 4

5 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 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. 5

6 Determine whether each graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. a. The graph shows the number of mail-order prescriptions. Answer: Positive correlation; with each year, the number of mail-order prescriptions has increased. 6

7 Determine whether each graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. b. The graph shows the percentage of voter participation in Presidential Elections. Answer: no correlation 7

8 The table shows the world population growing at a rapid rate. Year Population (millions)

9 Draw a scatter plot and determine what relationship exists, if any, in the data. 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. 9

10 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. 10

11 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 1 Find the slope. Slope formula Let and Simplify. 11

12 Step 2 Use m = 33.1 and either the point-slope form or the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000). Point-slope form Slope-intercept form Answer: The equation of the line is. 12

13 Check Check your result by substituting (1998, 5900) into Line of fit equation Replace x with 1998 and y with Multiply. Subtract. The solution checks. 13

14 The table shows the number of bachelor s degrees received since Years Since Bachelor s Degrees Received (thousands) Source: National Center for Education Statistics 14

15 a. Draw a scatter plot and determine what relationship exists, if any, in the data. Answer: The scatter plot seems to indicate that as the number of years increase, the number of bachelor s degrees received increases. There is a positive correlation between the two variables. 15

16 b. Draw a line of best fit for the scatter plot. c. Write the slope-intercept form of an equation for the line of fit. Answer: Using (4, 1137) and (10, 1184), 16

17 Use the prediction equation where x is the year and y is the population (in millions), to predict the world population in Answer: 6,296,000,000 Original equation Replace x with Simplify. 17

18 Use the equation where x is the years since 1988 and y is the number of bachelor s degrees (in thousands), to predict the number of bachelor s degrees that will be received in Answer: 1,204,000 18