Lesson 1-6

Example 1
EDUCATION  The mean SAT math scores for college-bound seniors is steadily increasing. The chart shows the mean SAT math scores from the years 1995 to 2002. Predict the mean SAT math score of college-bound seniors in the year 2008.
	Year	Mean SAT Math Scores	
	1995	506	
	1996	508	
	1997	511	
	1998	512	
	1999	511	
	2000	514	
	2001	514	
	2002	516	

Graph the data. Use the year as the independent variable and the mean SAT math score as the dependent variable.

Select two points that appear to represent the data. We chose (1996, 508) and (2001, 514). Determine the slope of the line.

Now use one of the ordered pairs, such as (1996, 508), and the slope in the point-slope form of the equation.

Thus, a prediction equation is y = 1.2x - 1887.2. Substitute 2008 for x to estimate the mean SAT math score for the year 2008.

According to this prediction equation, the mean SAT math score will be 522 in the year 2008. Use a different pair of points to find another prediction equation. How does it compare with this one?

Example 2
The table contains the barometric pressure and wind speeds of the Atlantic hurricanes and tropical storms that developed in 1998.

a.	Use a graphing calculator to find the equation of the regression line and the Pearson product-moment correlation.

b.	Use the equation to predict the wind speed of a hurricane whose barometric pressure is 950 millibars.	Hurricane/
Tropical Storm	Barometric Pressure (millibars)	Wind Speed (knots)	
	Alex	1000	45	
	Bonnie	954	100	
	Charley	1003	50	
	Danielle	955	90	
	Earl	986	85	
	Frances	990	55	
	Georges	938	130	
	Hermine	999	40	
	Ivan	975	80	
	Jeanne	970	90	
	Karl	970	90	
	Lisa	987	65	
	Mitch	905	155	
	Nicole	979	75	

a.	Enter the data for the barometric pressures in L1 and the data for wind speeds in list L2. Draw a scatter plot relating the barometric pressure, x, and the wind speed, y.

Then use the linear regression statistics to find the equation of the regression line and the correlation coefficient.
		
The Pearson product-moment correlation is about -0.97. The correlation between barometric pressure and wind speed is strongly negative. Because of the strong relationship, the equation of the regression line can be used to make predictions.

b.	When rounding to the nearest tenth, the equation of the regression line is
y = -1.15x + 1195.9. Thus, a hurricane whose barometric pressure is 950 millibars would have wind speeds of about
y = -1.15(950) + 1195.5 or 103.4 knots.