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

A scatter plot shows relationships between two sets of data.

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

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.

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

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.

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.

Practice Problem… The Olympic Games Discus Throw Year Winning throw 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 Let y represent the winning throw. View scatter plot on handout.

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

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

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 = 8 / 7 (88) + b = 704 / 7 + b = ≈ b = b

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 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.