1. Scatter Plots and Lines of Fit (4-5) Objective: Investigate relationships between quantities by using points on scatter plots. Use lines of fit to make and evaluate predictions.

2. Investigate Relationships Using Scatter Plots Data with two variables are called bivariate data. A scatter plot shows the relationship between a set of data with two variables, graphed as ordered pairs on a coordinate plane. Scatter plots are used to investigate a relationship between two quantities.

3. Correlation Correlation describes how well a line fits the data. There are three types of correlation: Positive correlation is when the points follow a positive slope. Negative correlation is when the points follow a negative slope. No correlation is when the points are so scattered that they cannot be best represented by a straight line.

4. Correlation Negative Correlation Positive Correlation No Correlation

5. Example 1 The graph shows the average number of students per computer in Maria’s school. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. Negative correlation As the years increase, the number of students per computer decreases.

6. Check Your Progress Choose the best answer for the following. The graph shows the number of mail- order prescriptions. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it. A.Positive correlation; with each year, the number of mail-order prescriptions has increased. B.Negative correlation; with each year, the number of mail-order prescriptions has decreased. C.No correlation D.Cannot be determined

7. Use Lines of Fit Scatter plots can show whether there is a trend in a set of data. When the data points all lie close to a line, a line of fit or trend line can model the trend. You can use a linear function to model data. 1.Make a scatter plot. Determine whether any relationship exists in the data. 2.Draw a line that seems to pass close to most of the data points. 3.Use two points on the line of fit to write an equation for the line. 4.Use the line of fit to make predictions.

8. Example 2 The table shows the growth of the world population. Identify the independent and dependent variables. Make a scatter plot and determine what relationship, if any, exists in the data. Independent Variable: Year Dependent Variable: Populations Positive Correlation As the years increase, the population increases. Year Populations (millions) 1650500 18501000 19302000 19754000 20046400

9. Example 3 Write an equation for the line of fit in example 2. Use the equation to predict the world’s population in 2025. (1850, 1000) and (2004, 6400) Year Populations (millions) 1650500 18501000 19302000 19754000 20046400 y – 1000 = 35.1(x – 1850) y – 1000 = 35.1x – 64935 +1000 y = 35.1x – 63,935 y = 35.1(2025) – 63,935 y = 71,077.5 – 63,935 y = 7142.5 million people

10. Check Your Progress Choose the best answer for the following. The table shows the number of bachelor’s degrees received since 1988. Draw a scatter plot and determine what relationship exists, if any, in the data. A.There is a positive correlation between the two variables. B.There is a negative correlation between the two variables. C.There is no correlation between the two variables. D.Cannot be determined. Years since 1988246810 Bachelor’s Degrees Received (thousands) 10511136116911651184

11. Check Your Progress Choose the best answer for the following. Draw a line of best fit for the scatter plot. Write the slope- intercept form of an equation for the line of fit. A.y = 8x + 1137 B.y = -8x + 1104 C.y = 6x + 47 D.y = 8x + 1104 (4, 1136) and (10, 1184) y – 1136 = 8(x – 4) y – 1136 = 8x – 32 +1136

12. Check Your Progress Choose the best answer for the following. 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 2015. A.1,320,000 B.1,112,000 C.1,224,000 D.1,304,000 2015 – 1988 = 27 years y = 8x + 1104 y = 8(27) + 1104 y = 216 + 1104 y = 1320 thousand