Correlation describes the type of relationship between two data sets. Unit 6 A scatter plot is a graph with points plotted to show a relationship between two sets of data. 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.

Negative correlation: as one data set increases, the other decreases. Unit 6 Negative correlation: as one data set increases, the other decreases. No correlation: changes in one data set do not affect the other data set. Positive correlation: both data sets increase together. Non-Linear: No straight line of best fit can be formed through the points.

Do the data sets have a positive, a negative, or no correlation? Unit 6 Do the data sets have a positive, a negative, or no correlation? The size of a jar of baby food and the number of jars of baby food a baby will eat. Negative correlation: The more food in each jar, the fewer number of jars of baby food a baby will eat.

Do the data sets have a positive, a negative, or no correlation? Unit 6 Do the data sets have a positive, a negative, or no correlation? The speed of a runner and the number of races she wins. Positive correlation: The faster the runner, the more races she will win.

Do the data sets have a positive, a negative, or no correlation? Unit 6 Do the data sets have a positive, a negative, or no correlation? The size of a person and the number of fingers he has. No correlation: The size of a person will not affect the number of fingers a person has.

Example 1: Making a Scatter Plot of a Data Set Unit 6 Example 1: Making a Scatter Plot of a Data Set Use the given data to make a scatter plot of the weight (y) and height (x)of each member of a basketball team, and describe the correlation. The points on the scatter plot are (71, 170), (68, 160), (70, 175), (73, 180), and (74, 190). There is a positive correlation between the two data sets.

There is a positive correlation between the two data sets. Unit 6 Example 2: Use the given data to make a scatter plot of the weight and height of each member of a soccer team, and describe the correlation. 200 190 180 170 160 150 140 130 120 Height (in) Weight (lbs) 63 125 67 156 69 175 Weight 68 135 62 120 The points on the scatter plot are (63, 125), (67, 156), (69, 175), (68, 135), and (62, 120). 60 61 62 63 64 65 66 67 68 69 Height There is a positive correlation between the two data sets.

Line of Best Fit… A line that comes close to all the points on a scatter plot. Hint: Try to draw the line so that about the same number of points are above the line as below the line.

Example 3: Using a Scatter plot to Make Predictions Unit 6 Example 3: Using a Scatter plot to Make Predictions Make a scatter plot of the data, and draw a line of best fit. Then use the data to predict how much a worker will earn in tips in 10 hours. Tips earned may be dependent on the number of hours worked. Step 1: Make a scatter plot. Let hours worked represent the independent variable x and tips earned represent the dependent variable y.

Additional Example 2 Continued Unit 6 Additional Example 2 Continued Step 2: Draw a line of best fit. Draw a line that has about the same number of points above and below it.

Additional Example 2 Continued Unit 6 Additional Example 2 Continued Step 3: Make a prediction. According to the graph, working 10 hours will earn about $24 in tips. Find the point on the line whose x-value is 10. The corresponding y-value is about 24.

Formative Assessment: Unit 6 Formative Assessment: Are you really getting scatter plots and lines of best fit?? 12

Unit 6 1. Use the given information to make a scatter plot, and describe the correlation. Grading Period 1 2 3 4 Number of A’s 5 6 8 10 positive correlation

Unit 6 2. Draw a line of best fit for the scatter plot you drew in Problem 1. Then use the data to predict the number of A’s in grading period 6. approximately 13 A’s

1. Identify a scatter plot for the given data. Unit 6 1. Identify a scatter plot for the given data. A. B. 15

2. Do the data sets have a positive, a negative, or no correlation? Unit 6 2. Do the data sets have a positive, a negative, or no correlation? distance covered and time taken at constant speed A. positive B. negative C. none 16

3. Do the data sets have a positive, a negative, or no correlation? Unit 6 3. Do the data sets have a positive, a negative, or no correlation? value of a used car and the total distance traveled A. positive B. negative C. none 17