For questions 3–4, use your calculator to create a scatter plot and line of best fit for the following set of data: Average height of a species of tree (in feet) after a certain number of years Years 1 2 3 4 5 6 7 8 Height 2.1 3.2 6.8 7.3 11.2 12.6 13.4 15.9 What is the correlation coefficient for the set of data? Round your answer to the nearest thousandth. (1 point) Responses 0.014 0.014 0.989 0.989 0.075 0.075
To find the correlation coefficient for the set of data, follow these steps:
1. Enter the years in List1 in your calculator and the corresponding heights in List2.
2. Go to the stat menu on your calculator and select "Edit" (or any similar option).
3. Enter the years in List1 and the heights in List2.
4. Go to the stat menu again and select "CALC" (or any similar option).
5. Choose "LinReg" or "LinReg(ax+b)" (linear regression) and press enter.
6. The calculator will output the equation of the line of best fit and the correlation coefficient (r).
The correlation coefficient for this set of data is 0.989.
To calculate the correlation coefficient for the given set of data, you can follow these steps:
Step 1: Enter the given data into two lists on your calculator. Label one list as "Years" and the other as "Height."
Years: 1, 2, 3, 4, 5, 6, 7, 8
Height: 2.1, 3.2, 6.8, 7.3, 11.2, 12.6, 13.4, 15.9
Step 2: On your calculator, calculate the correlation coefficient. Specific steps may vary depending on the type of calculator you are using, but the general procedure is as follows:
- Press the "STAT" button on your calculator.
- Select "Edit"
- Input the Years data into one list.
- Input the Height data into another list.
- Go back to the "STAT" menu and select "CALC."
- Choose "LinReg(ax+b)" or "LinReg(a+bx)" option.
- Press "Enter" or "Calculate" to get the correlation coefficient.
Step 3: Round your answer to the nearest thousandth.
The correlation coefficient for the given data is 0.989.
To calculate the correlation coefficient for the set of data and create a scatter plot with a line of best fit, you will need a graphing calculator capable of performing regression analysis.
Here's how you can do it on a TI graphing calculator:
1. Enter the given data into the statistics lists on your calculator, with the years in one list and the corresponding heights in another.
2. To create a scatter plot, go to the "STAT PLOT" menu. Enable a plot by selecting "ON." Choose the type of plot you want, which is usually scatter plot indicated as "1." Assign the lists you just entered the data into as the X and Y variables for the plot.
3. Once you have the scatter plot displayed on your calculator screen, you can calculate the line of best fit. Go to the "CALC" menu and select "LinReg(ax+b)" or a similar option. This will calculate the equation of the line that best fits the data.
4. After the calculator performs the regression analysis, it will display the equation of the line, which will be in the form "Y = aX + b" where "a" represents the slope (rate of change) and "b" represents the y-intercept. Take note of these values.
5. Now, to find the correlation coefficient, go to the "STAT" menu, and select "CALC." Choose either "LinReg" or "LinRegTtest" depending on the calculator model.
6. The calculator will return the correlation coefficient, also known as the coefficient of determination (r^2). Round the value to the nearest thousandth, as requested in the question.
So, based on this procedure, the correlation coefficient for the given set of data is 0.989 (rounded to the nearest thousandth).