Use a graphing calculator and find the correlation coefficient r between two variable in the table below
(1,21),(2,26),(3,35),(4,37)(5,40)
To find the correlation coefficient (r) using a graphing calculator, follow these steps:
1. Enter the given data into the calculator in the form of two lists: one for the x-values and one for the corresponding y-values. The lists should be of the same length and should preserve the order of the data points. The data for the given problem should be entered as follows:
List1: {1, 2, 3, 4, 5}
List2: {21, 26, 35, 37, 40}
2. Go to the statistics menu on the calculator. The exact steps to access the statistics menu may vary depending on the calculator model, but it is generally denoted by a symbol such as "STAT" or "STATS." Press the appropriate key to enter the statistics menu.
3. In the statistics menu, select the option for conducting a regression analysis. This option is commonly labeled as "Regression" or "LinReg." Choose the appropriate regression analysis for the given data, in this case, linear regression (LinReg).
4. After selecting linear regression, the calculator will display regression statistics, including the correlation coefficient (r). The correlation coefficient is denoted by the letter "r" and should be a value between -1 and 1. In this example, the calculator should display the correlation coefficient as:
r = 0.9638
Therefore, the correlation coefficient (r) for the given data is approximately 0.9638.
To find the correlation coefficient (r) between two variables using a graphing calculator, we need to follow these steps:
Step 1: Enter the data into the calculator. For this example, we have the following data points:
(1, 21), (2, 26), (3, 35), (4, 37), (5, 40)
Step 2: Create a scatter plot of the data. We can use the calculator's graphing functions to plot the points on a graph.
Step 3: Calculate the correlation coefficient (r) using the regression feature. Most graphing calculators have a built-in regression analysis feature. We will use this to find r.
Here are the step-by-step instructions for finding the correlation coefficient using a few popular graphing calculators:
TI-84 Plus/TI-83 Plus calculators:
1. Press the [STAT] button to enter the statistics menu.
2. Enter the x-values into L1 and the y-values into L2.
3. Press the [2nd] button, then [STATPLOT].
4. Select a graphing option (e.g., Scatter Plot) and press [ENTER].
5. Press [ZOOM], then [9] to zoom to fit the data on the screen.
6. Press the [STAT] button again to re-enter the statistics menu.
7. Select [CALC] and then [4: LinReg(ax+b)] to perform linear regression.
8. Press [ENTER] to calculate the regression equation and statistical values.
9. The correlation coefficient (r) will be displayed as "r=" on the calculator screen.
Texas Instruments Nspire calculators:
1. Press the [MENU] button.
2. Select [Statistics] and then [Statistical Calculations].
3. Choose [RegEQ] for regression calculations.
4. Enter the x-values and y-values.
5. Press [ENTER] to calculate the regression equation and statistical values.
6. The correlation coefficient (r) will be displayed as "Coefficient r" on the calculator screen.
Casio calculators:
1. Press the [MODE] button to enter the statistics mode.
2. Enter the x-values into a variable (e.g., X) and the y-values into another variable (e.g., Y).
3. Press the [AC] (or [CLR] or [DEL]) button to clear the screen.
4. Enter the regression command. For example, type: "REGR X,Y" and press [EXE].
5. The correlation coefficient (r) will be displayed as "r" on the calculator screen.
After following the steps specific to your calculator, you should obtain the correlation coefficient (r) value.
To find the correlation coefficient (r) between two variables using a graphing calculator, you can follow these steps:
1. Enter the given data points into your graphing calculator.
- For this example, enter the x-values (1, 2, 3, 4, and 5) into one list and the corresponding y-values (21, 26, 35, 37, and 40) into another list.
2. Calculate the linear regression equation for the data.
- On most graphing calculators, you can find this by accessing the STAT menu, then selecting "Lreg" or "LinReg" to perform linear regression on the data.
- This will give you an equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
3. Once you have the linear regression equation, your calculator should also display the correlation coefficient (r).
- The correlation coefficient is usually denoted by the letter r and ranges between -1 and +1, with positive values indicating a positive relationship and negative values indicating a negative relationship. A correlation coefficient of 0 indicates no relationship between the variables.
By following these steps, you can easily find the correlation coefficient (r) using a graphing calculator.