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Warm-Up

Warm-Up. CD SINGLES. The table shows the total number of CD single shipped (in millions) by manufacturers for several years during the period 1993 – 1997 . Create a scatter plot of the data. Remember x is the independent variable y is the dependent variable. Homework Review.

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Warm-Up

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  1. Warm-Up CD SINGLES The table shows the total number of CD single shipped (in millions) by manufacturers for several years during the period 1993–1997. • Create a scatter plot of the data. • Remember • x is the independent variable • y is the dependent variable

  2. Homework Review

  3. Quiz 5.1 – 5.4 • When you are done with the quiz do not hand it in. I will collect it when everyone is done.

  4. Warm Up • Write an equation in slope-intercept form of the line that passes through the points. • (5, 32), (7,16) • (0, 160), (25, 610) 3. (-12, -15), (-18, -12) y = -8x + 72 y = 18x + 160 y= -1/2x - 21

  5. FITTING A LINE TO DATA 8 6 4 2 –8 –6 –4 –2 0 2 4 6 –2 –4 –6 –8 There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach. Usually, there is no single line that passes through all the data points, so you try to find the line that best fits the data. This is called the best-fitting line. best-fitting line.

  6. 250 DISCUS THROWS 240 230 220 210 200 190 180 Distance (ft) 170 160 150 140 130 120 110 100 0 8 16 24 32 40 48 56 64 72 80 88 96 104 Years since 1900 The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws. Write an equation of your line.

  7. (96, 230) 250 240 230 220 (8, 138) 210 (96, 230). 200 190 180 Distance (ft) 170 160 150 140 (8, 138) 130 120 110 100 0 8 16 24 32 40 48 56 64 72 80 88 96 104 Years since 1900 SOLUTION Find two points that lie on the best-fitting line, such as (8, 138) and (96, 230). Find the slope of the line through these points.

  8. (96, 230) 250 y2–y1 92 88 230–138 240 = 1.05 230–138 m = 92 88 1.05 = = = 96–8 x2–x1 230 96–8 220 210 200 190 180 Distance (ft) 170 160 150 140 (8, 138) 130 120 An equation of the best-fitting line isy = 1.05x + 129.6. 110 In most years, the winner of the discus throw was able to throw the discus farther than the previous winner. 100 0 8 16 24 32 40 48 56 64 72 80 88 96 104 Years since 1900 y = mx+b Write slope intercept form. Substitute 1.05 for m, 8 for x, 138 for y. 138= (1.05)(8) + b 138 = 8.4 + b y = mx+b Simplify. Solve for b. 129.6 =b

  9. DETERMINING THE CORRELATION OF X AND Y In this scatter plot, x and yhave a positive correlation, which means that the points can be approximated by a line with a positive slope.

  10. DETERMINING THE CORRELATION OF X AND Y In this scatter plot, x and y have a negative correlation, which means that the points can be approximated by a line with a negative slope.

  11. DETERMINING THE CORRELATION OF X AND Y In this scatter plot, x and y have relatively no correlation, which means that the points cannot be approximated by a line.

  12. TYPES OF CORRELATION DETERMINING THE CORRELATION OF X AND Y Positive Correlation Negative Correlation No Correlation

  13. Draw a scatter plot of the data. State the type of correlation that the data has. If possible, draw a line that closely fits the data and write an equation of the line. 1. 2. 3. No Correlation Negative Correlation Positive Correlation y = -1.54x + 3.23 y = 1.10x + 3.68

  14. Practice: workbook 5-4

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