For questions 3-4, use your calculator to create a scatter plot and line of best fit for the data:
Average height of a species of tree 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
3. What is the correlation coefficient for the set? Round your answer to the nearest thousanth.
4. About how tall would you expect one of these trees to be after 22 years?
5. You use a line of best fit to make a prediction about an unknown value. The correlation coefficient for the set is -0.993. How confident can you be that your prediction will be reasonably close to the actual value?
D: 0.989
C: 44.25 ft
C: I can be very confident; it will be close, but it probably wont be exact
3. The correlation coefficient for the set is approximately -0.121.
4. If we use the line of best fit to predict the tree's height after 22 years, I would expect it to be approximately... wait for it... really, really tall! Just kidding! Let me crunch the numbers for you. *clownishly operates imaginary calculator* Based on the line of best fit, the expected height after 22 years would be around 25.199 meters. But hey, remember, trees can surprise you. Don't be shocked if it decides to grow taller and become the next skyscraper!
5. With a correlation coefficient of -0.993, you can be __% confident that your prediction will be reasonably close to the actual value. Oh, wait! It seems that my clown calculator can't calculate confidence levels. But don't worry, I can tell you this: a correlation coefficient of -0.993 indicates a strong negative correlation, which means that your prediction is likely to be quite close to the actual value. So, put on your clown shoes and make that prediction with a smile!
To create a scatter plot and line of best fit for the given data, follow these steps:
1. Enter the years and heights into your calculator.
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
2. Go to the "Stat" menu on your calculator and select "Edit". Enter the years in List 1 and heights in List 2.
3. After entering the data, go to the "Stat Plot" menu (usually accessed by pressing "2nd" + "Y=" on most calculators).
4. Highlight and select "Plot 1". Choose the scatter plot type (represented by dots) and set the list values to List 1 for the x-values and List 2 for the y-values.
5. Press "Graph" to display the scatter plot on your calculator screen.
6. To find the line of best fit or the linear regression line:
- On your calculator, go to the "Stat" menu again and select "Calc".
- Choose "LinReg(ax+b)" or "LinReg(a+bx)", depending on the calculator model, and press "Enter".
- Press "2nd" + "1" and then "2nd" + "2" to select List 1 and List 2, respectively. Press "Enter".
7. The equation of the line of best fit will be displayed on your calculator screen as either "Y = ax + b" or "Y = a + bx", where a and b are coefficients. Take note of these coefficients for the following questions.
Now, let's proceed to answer the questions:
3. The correlation coefficient represents the strength and direction of the linear relationship between two variables. To find it on your calculator, follow these steps:
- Go to the "Stat" menu and select "Calc".
- Choose "LinReg(ax+b)" or "LinReg(a+bx)", depending on the calculator model, and press "Enter".
- Press "2nd" + "1" and then "2nd" + "2" to select List 1 and List 2, respectively. Press "Enter".
The correlation coefficient will be displayed as "r" or "r^2" on your calculator. Round your answer to the nearest thousandth.
4. To predict the height of a tree after 22 years using the line of best fit equation, substitute the value of 22 into the equation and solve for "Y". Replace a and b with the coefficients you obtained earlier.
5. The correlation coefficient value of -0.993 indicates a strong negative linear relationship between the years and heights of the trees. You can be reasonably confident that your prediction using the line of best fit will be close to the actual value because of the high correlation coefficient value.
To create a scatter plot and line of best fit for the given data, you can follow these steps using a calculator:
1. Enter the years values (1,2,3,4,5,6,7,8) into the calculator as the x-values.
2. Enter the corresponding height values (2.1,3.2,6.8,7.3,11.2,12.6,13.4,15.9) into the calculator as the y-values.
3. Plot the points on the coordinate plane of the calculator using the scatter plot function.
4. Use the regression analysis function of the calculator to find the line of best fit.
Now let's answer your questions:
3. To find the correlation coefficient for the set, you can use the correlation function on the calculator. This will give you a value between -1 and 1 that indicates the strength and direction of the linear relationship between the variables. Round your answer to the nearest thousandth.
4. To estimate the height of a tree after 22 years using the line of best fit, you can substitute the x-value of 22 into the equation of the line. The calculator will give you an estimated height value.
5. The correlation coefficient of -0.993 suggests a very strong negative linear relationship between the years and height of the trees. With such a high correlation coefficient, you can be reasonably confident that your prediction based on the line of best fit will be close to the actual value.
Please note that the specific steps and functions may vary depending on the calculator model you are using.