1. Learn to create and interpret scatter plots and find the line of best fit. 5.4 Scatter Plots

2. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to interpret linear models. - Interpret slope in context of data. - Write the line-of- best-fit for a scatter plot. - Distinguish between correlation and causation. - Use technology to calculate correlation coefficient. The student will be able to: - Determine if a scatter plot has positive or negative correlation and if the correlation is weak or strong. - Use the correlation coefficient to interpret the strength of a correlation. With help from the teacher, the student has partial success interpreting linear models or scatter plots. Even with help, the student has no success understandi ng the concept of a linear models. Learning Goal #2 for Focus 4 (HS.S-ID.C.7, 8 & 9, HS.S- ID.B.6, HS.F-IF.B.6): The student will be able to interpret linear models.

3. A scatter plot shows relationships between two sets of data.

4. Use the given data to make a scatter plot of the weight and height of each member of a basketball team. Making a Scatter Plot of a Data Set The points on the scatter plot are (71, 170), (68, 160), (70, 175), (73, 180), and (74, 190). Example 1

5. Correlation describes the type of relationship between two data sets. The line of best fit is the line that comes closest to all the points on a scatter plot. One way to estimate the line of best fit is to lay a ruler’s edge over the graph and adjust it until it looks closest to all the points.

6. Positive correlation; both data sets increase together. Negative correlation; as one data set increases, the other decreases. No correlation

7. Finding the Line of BEST Fit Usually there is no single line that passes through all the data point, so you try to find the line that best fits the data. Step 1: using a ruler, place it on the graph to find where the edge of the ruler touches the most points. Step 2: Draw in the line. Make sure it touches at least 2 points.

8. Finding the Line of BEST Fit (continued) Step 3: Find the slope between two points Step 4: Substitute that into slope-intercept form of an equation and solve for “b.” Step 5: Write the equation of the line in slope-intercept form.

9. Practice Problem… The Olympic Games Discus Throw Year Winning throw 1908 134.2 1912 145.1 1920 146.6 1924 151.4 1928 155.2 1932 162.4 1936 165.6 1948 173.2 1952 180.5 1956 184.9 1960 194.2 1964 200.1 1968 212.5 1972 211.4 1976 221.5 1980 218.7 1984 218.5 1988 225.8 1992 213.7 1996 227.7 The Olympic games discus throws from 1908 to 1996 are shown on the table. Approximate the best - fitting line for these throws let x represent the year with x = 8 corresponding to 1908. Let y represent the winning throw. View scatter plot on handout.

10. Step 1 & 2: Place your ruler on the page and draw a line where it touches the most points on the graph.

11. Step 3: Find the slope between 2 points on the line. The line went right through the point at 1960 and 1988. The ordered pairs for these points are (60, 194.2) and (88, 225.8). m = y 2 – y 1 = 225.8 – 194.2 = 31.6 = 32 =8 x 2 – x 1 88 – 60 28 28 7 m = 8 7

12. Step 4: Find the y-intercept. Substitute the slope and one point into the slope-intercept form of an equation. Slope: 8 / 7 and point: (88, 225.8) y = mx + b 225.8 = 8 / 7 (88) + b 225.8 = 704 / 7 + b 225.8 = ≈100.6 + b -100.6 -100.6 125.2 = b

13. Step 5: Write in slope-intercept form. Substitute each value into y = mx + b. The equation of the line of best fit is: y = 8 / 7 x + 125.2 When you solve these problems, you can get different answers for the line of best fit if you choose different points. But the equations should be close.

14. Talk About It Partner #1 Tell what a scatter plot is and what relationship it conveys. Partner #2 Tell the steps of how to write the equation of the line of best fit for a scatter plot.