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Example Equation: y=-2.5x+16.5
Predicted Number of Wins: Approximately 2
| ERA | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 5 |
|---|---|---|---|---|---|---|---|---|
| Number of Wins | 14 | 12 | 10 | 10 | 9 | 7 | 6 | 4 |
Let's construct a scatter plot of the given data. We will treat each ERA and the corresponding number of wins as an ordered pair and draw it in the coordinate plane. We will put the ERA on the x-axis and number of wins on the y-axis.
We can see that the number of wins decreases when the ERA increases. This means that there is a negative association.
Now, let's find the equation of the trend line. To do so we will identify the y-intercept and the slope.
We can see that the y-intercept is about 16.5 and the slope is - 104. By using this information we are able to write an equation of our trend line. y= -10/4x+ 16.5 ⇕ y=-2.5x+16.5 Finally, we want to predict the number of wins of a pitcher with an ERA of 6. To do this, we will substitute 6 for x into our equation.
x= 6
(- a)b = - ab
Add terms
Round to nearest integer
We can predict that a pitcher with an ERA of 6 will win about 2 times. Notice that this is only an example solution, because we can draw other trend lines that fit the situation.
