Draw the trend line near the data points and write the equation by using the points that appear on the line.
C
c
Use the equation from Part B.
D
d
Consider the trend line and the line equation from Part B. Make a prediction about the new trend line.
A
a
Scatter Plot:
B
b
Example Trend Line:
Example Equation: y=0.9x+19 100.2
C
c
U.S. Female Population: About 154 100 200
D
d
Yes, it would be reasonable. See solution.
Practice makes perfect
a
We have been given the following table that shows the estimated population of the United States.
Estimated Population of the United States (thousands)
Year
2000
2001
2002
2003
2004
2005
2006
Male
138 482
140 079
141 592
142 937
144 467
145 973
147 512
Female
143 734
145 147
146 533
147 858
149 170
150 533
151 886
We will make a scatter plot of the data pairs using (male population, female population). Let's start by plotting the data. Let the x-axis represent the male population and the y-axis represent the female population.
We can write an equation for this line of fit in slope-intercept form.
y= mx+ bIn this form, m is the slope and b is the y-intercept. First, let's find the slope by using the Slope Formula.
m=y_2-y_1/x_2-x_1
Here (x_1,y_1) and (x_2,y_2) represent the points that are on the line. There are many points appear to be on the line, but let's choose (138 482,143 734) and (147 512,151 886) and substitute them into the formula.
The slope for the line of fit is approximately 0.9.
y=0.9x+ b
Next, we will find the y-intercept by substituting the point (138 482,143 734) into this equation.
Finally, we can write the complete equation for our trend line.
y=0.9x+19 100.2
c
Now, we will use our equation from Part B to predict the U.S. female population if the U.S. male population increases to 150 000 thousand. In order to do that, we will substitute 150 000 for x and find y.
Let's consider the scatter plot of the data pairs (year, male population). Since the U.S. male population increases over time, a trend line of the scatter plot will be similar to the one that we made in Part B. Therefore, it would be reasonable to use this scatter plot.
