To calculate the correlation coefficient [tex]\( r \)[/tex] between the study hours and GPA using a T1-83, T1-83 Plus, or T1-84 graphing calculator, follow these steps:
1. Enter Data:
- Press the `STAT` button.
- Select `1:Edit` to enter data into lists.
- Enter the study times into list [tex]\( L1 \)[/tex] and GPAs into list [tex]\( L2 \)[/tex]. Make sure each pair (study time and corresponding GPA) is entered in a corresponding position in both lists.
[tex]\[ L1: 13.6, 1.6, 5.1, 1.7, 10.2, 19.7, 7.6, 0.5, 4.4, 19.2 \][/tex]
[tex]\[ L2: 3.58, 2.37, 2.57, 2.28, 3.68, 3.69, 3.17, 2.03, 2.56, 3.51 \][/tex]
2. Calculate Correlation Coefficient:
- After ensuring that all data pairs are entered correctly, press `STAT` again.
- Navigate to the `CALC` menu.
- Select `4:LinReg(ax+b)` and press `ENTER`.
- It will display the linear regression equation. Ensure that the lists [tex]\( L1 \)[/tex] and [tex]\( L2 \)[/tex] are used:
[tex]\[ LinReg(ax+b) \, L1, L2 \][/tex]
- Press `ENTER` to execute the calculation.
3. Interpretation of Result:
- The calculator will display several statistics, including [tex]\( a \)[/tex] (the slope), [tex]\( b \)[/tex] (the y-intercept), and [tex]\( r \)[/tex] (the correlation coefficient).
4. Round the Correlation Coefficient:
- Locate the value of [tex]\( r \)[/tex]. This is the correlation coefficient.
- Round this value to two decimal places to get the final answer.
In this case, the correlation coefficient [tex]\( r \)[/tex] is found to be:
[tex]\[ r = 0.90 \][/tex]
So, the correlation coefficient between the hours studied and GPA, rounded to two decimal places, is [tex]\( 0.90 \)[/tex].
