c Think about the context of the problem and what x and y represent.
A
a
Line of Best Fit: y=381x-566 Graph:
B
b r=0.989, strong positive correlation.
C
c See solution.
Practice makes perfect
a We have been given a table with data for x and y.
Minutes, x
People, y
1
10
2
100
3
400
4
900
5
1400
6
1800
7
2100
In order to find a line of fit using our calculator, we need to first enter the values. Let's press the STAT button.
Then we choose the first option in the menu, Edit, and fill in the values in lists L1 and L2.
We can perform a regression analysis on the data by pressing the STAT button again, followed by using the right-arrow key to select the CALC menu.
This menu lists the various regressions that are available. If we choose the fourth option in the menu LinReg(ax+b) and press ENTER, the calculator performs a linear regression using the data that was entered.
We will substitute the values of a and b into the equation y= ax+ b to find the equation of the line of best fit.
y= 381x -566
Next we want to graph the data and the line of fit on the same coordinate plane. Let's press Y= on the calculator. Then we write the equation on one of the rows.
To adjust the viewing window we press the button WINDOW and set the values to fit our data.
To make the calculator graph both the line and the scatter plot we need to press STAT PLOT.
If the scatter plot is Off or if we want to change any settings we press ENTER.
To activate the scatter plot place the cursor on the option On and press ENTER. We need to select the first symbol in Type to get a scatter plot. We can now draw the scatter plot and the line of fit by pressing GRAPH.
b The correlation coefficient is represented with the variable r. Let's consider the linear regression output.
We find the correlation coefficient in the last row.
r= 0.989
The correlation coefficient r is always between -1≤ r≤1, where positive values represent a positive slope and negative values represent a negative slope. Additionally, the closer the value is to 0, the weaker the correlation. Our value, r= 0.989, tells us that the correlation is positive and strong.
c In Part A, we found the equation for the line of best fit.
y= 381x -566
We know that the slope is 381 and the y-intercept is -566. To interpret these values we need to understand that x is the number of minutes that have passed and y is the number of people who reported feeling the earthquake. Recall that slope is the change in y divided by the change in x.
Slope&= 381
&⇕
Δ y/Δ x&=381people/1minute
This means that on average 381 people reported the earthquake each minute after it hit. The y-intercept does not actually make any sense in the context of the problem, as there cannot be a negative number of people reporting the earthquake. It is an extension of the line beyond reasonable boundaries.
