b The correlation coefficient is r in the linear regression output on your graphing calculator.
C
c Does the number of volunteers increase or decrease over time? Can we predict how many volunteers came on a day before the first day of the given data?
A
aLine of Best Fit: y=x+7
Graph:
B
bCorrelation Coefficient: r=0.619
Interpretation: A moderately strong, positive correlation
C
c See solution.
Practice makes perfect
a We have been given a table with data for x and y.
Day, x
1
2
3
4
5
6
7
8
People, y
9
5
13
11
10
11
19
12
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 can round the value of b and substitute it along with a into the equation y= ax+ b. This gives us the equation for the line of best fit.
y= 1x+ 7 ⇔ y=x+7
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 enable that the calculator graphs both the line and the scatter plot we need to press STAT PLOT.
If the scatter plot is Off/q> or if we want to change any settings we press ENTER.
To activate the scatter plot, we place the cursor on the option On and press ENTER. We also need to select the first symbol from 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= 0.6194
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= 0.6194, tells us that the correlation is positive and moderately strong.
c In Part A we found the equation for the line of best fit.
y=x+7
In this equation, the slope is 1 and the y-intercept is 7.
The slope tells us that, on average, the number of volunteers at the animal shelter is increasing by approximately 1 person each day.
The y-intercept gives us a prediction for the number of volunteers on the day before the first day, where x=0.
