Line of Best Fit: y=-0.08x+3.8 Correlation Coefficient: r=-0.965 Interpretation: A strong, negative correlation
B
b See solution.
C
c 2.7
D
d See solution.
Practice makes perfect
a We have been given a table with data for x and y.
Hours, x
Grade Point Average, y
10
3.0
5
3.4
3
3.5
12
2.7
20
2.1
15
2.8
8
3.0
4
3.7
16
2.5
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 values of a and b and substitute them into the equation y= ax+ b. This gives us the equation for the line of best fit.
y= -0.08 x+ 3.8
The correlation coefficient is r≈ -0.965. Since r is very close to -1, we know that there is a strong, negative correlation.
b In Part A we found that the equation of the line of best fit is y= -0.08x+ 3.8. Let's identify its slope and y-intercept.
Slope: m= -0.08
y-intercept: b= 3.8
To interpret the slope, we need to understand that x is the hours of TV watched by the student each week and y is their GPA. Recall that slope is the change in y divided by the change in x.
Δ y/Δ x=-0.08grade points/1hours of TV
This means that the students' GPAs drop -0.08 points for each hour of TV watched per week. A y-intercept of 3.8 tells us that students who watch 0 hours of TV each week should have a GPA around 3.8.
c To predict the GPA of a student who watches 14 hours of television each week, we can substitute x= 14 into our line of best fit.
There is causation between two variables when a change in one variable causes a change in the other.
GPA is dependent on how much time is spent on studying. This means that causation will exist if watching less TV also means studying more. Let's say that a student makes a decision to watch less TV. If the time is spent on studying it will probably affect GPA, but if the student instead spends the time on hanging out with friends, it will not affect GPA.
