c Find and use the equation for the trend line traced in Part B.
D
d How can you tell if a data set has a strong or weak correlation?
A
a
B
bExample Trend Line:
C
c Around 6.5 million licensed drivers.
D
d See solution.
Practice makes perfect
a We can find the table showing population and licensed driver statistics below.
Licensed Drivers
State
Population (millions)
Number of Drivers (millions)
Arkansas
2.8
2.0
Illinois
12.8
8.1
Kansas
2.8
2.0
Massachusetts
6.4
4.7
Pennsylvania
12.4
8.5
Texas
23.5
14.9
To make a scatter plot we just need to plot the data as ordered pairs.
b Recall that a trend line is a line that approximates the relationship between the variables in a scatter plot. We can trace one by using any two data points. Therefore, there is no unique trend line. We can trace one line passing through the points (2.8,2.0) and (23.5,14.9).
c In order to use our model to predict the number of licensed drivers, we first need to find the equation of our trend line. Recall that in Part B we used the points (2.8,2.0) and (23.5,14.9) to trace it. We can start by finding the slope using the Slope Formula.
m = y_2-y_1/x_2-x_1
In this formula (x_1,y_1) and (x_2,y_2) are two known points. Let's try finding the slope for our trend line.
We find that the slope for our trend line is approximately 0.63. Now we can use the point-slope form. In this form (x_1,y_1) is a known point, and m is the slope of the line.
y-y_1=m(x-x_1)
We can substitute either of our known points and the slope value we found before. We will use the point (2.8,2.0). We can also isolate y so that evaluating our equation becomes easier.
Now we can use our equation to predict the number of licensed drivers for a population of 10 million people. For this, we evaluate our function when x=10.
As we can see, our model predicts that there would be around 6.5 million licensed drivers. Notice that, as there is no unique trend line for this data set, there is no unique correct answer. However, other trend lines choices should predict similar results.
d We can say that the population and the number of licensed drivers is strongly correlated, as all the data points lie very close along a line. We can see this clearer in Part B, where we traced an example trend line.
