Objectives: 1) Scatter plot and linear equations

2) Using the line of the best fit to make future prediction

Scatter plot: a graph that relates data from two different sets.

Scatter plots will often show at a glance whether a relationship exists between two sets of data.

Warm up Question:

Describe the type of correlation between x and y for each scatter plot.

a)  b)

c) d)

Correlation Coefficient:

The correlation coefficient is a number from -1 to 1.

The sign of r indicates the direction of the relationship between the variables.

If r is a positive, the slope of the line is positive. If r is a negative, the slope of the line is negative.

The absolute value of the correlation coefficient indicates the strength of the linear relationship. The closer r to 1 the stronger the linear relationship is. The closer r to 0 indicates there is no relationship between the variables.

Line of best fit is the trend line that shows the relationship between two sets of data most accurately.

Practice 1:

The table shows the percent of U.S. workers in Farm Occupations.

Years since 1900
/ 0 / 20 / 40 / 60 / 80 / 94
Farm Workers / 37.5 / 27 / 17.4 / 6.1 / 2.7 / 2.5
Source: The World Almanac

a) Draw a scatter plot and determine what relationship exists if any, in the data.

b) Draw a line of the best fit for the scatter plot.

c) Write the slope-intercept form of an equation for the line of fit.

d) Use the equation for the line of fit to estimate the percent of U.S. workers in farm occupations in 1996.

Practice 2:

HEALTH The table below shows the total amount of money spent on health care, in billions of dollars, for the years 1970 through 1998.

Year / 1970 / 1980 / 1990 / 1998
Billions of $ / 73.2 / 247.3 / 699.4 / 1149.1

a) Draw a scatter plot and a line of fit for the data.

b) Find a prediction equation. What do the slope and y-intercept indicate?

c) Predict the amount of money spent on health care in 2005.