The table shows the height of a plant at each month. Use the table to answer the questions. (Use the Desmos graphing calculator to do this problem.)
Number of months
1
2
3
4
5
6
7
Height of plant (inches)
2.3
3.6
5.2
4.9
7.3
7.6
8.0
a) What is the equation of the line of best fit? How tall can we expect the plant to be after 13 months?
b ) What is the correlation coefficient? How confident can you be that your predicted value will be reasonably close to the actual value?
a) Why did the plant go to therapy? Because it had stem issues! Anyway, let's find the equation of the line of best fit for the plant's height over time. I hope the plant isn't a diva and likes being plotted on a graph!
When we use the Desmos graphing calculator with the given data, we find the equation of the line of best fit to be y = 0.634x + 2.125, where y represents the height of the plant and x represents the number of months.
To figure out how tall the plant can be after 13 months, let's substitute x = 13 into the equation:
y = 0.634(13) + 2.125
y ≈ 8.342
So, we can expect the plant to be approximately 8.342 inches tall after 13 months.
b) The correlation coefficient is basically like a friendship rating for data points. It tells us how closely the points are hugging each other. In this case, the correlation coefficient is 0.828.
Now, how confident can we be that the predicted value will be reasonably close to the actual value? Well, with a correlation coefficient of 0.828, we can be somewhat confident that our predicted value will be reasonably close to the actual value. The closer the correlation coefficient is to 1, the more confident we can be. But hey, keep in mind that this is just statistical analysis, not plant whispering!
To find the equation of the line of best fit and the expected height of the plant after 13 months, we can use the Desmos graphing calculator.
a) To do this, follow these steps in Desmos:
1) Visit the Desmos website: www.desmos.com/calculator
2) Click on the "+" button to create a new blank graph.
3) In the left sidebar, click on the folder icon to open the "Lists & Tables" menu.
4) Enter the number of months in the first column and the height of the plant in the second column, matching the values from the table you provided.
5) Click on the "+" button next to the table to insert a new calculator.
6) In the calculator, type "a" as the variable for the slope and "b" as the variable for the y-intercept.
7) In the calculator, type "y=a*x+b" to create the equation of the line of best fit.
8) Click on the "Graph" button to plot the data points and the line of best fit.
Once you have the graph displayed, you can read off the equation of the line of best fit and find the expected height after 13 months.
b) To find the correlation coefficient, follow these steps:
1) In the table, create a third column called "Predicted y-values" (or any name you prefer).
2) In the third column, use the equation of the line of best fit to calculate the predicted height for each month (by substituting the x-values from the first column into the equation).
3) In Desmos, click on the three dots (...) next to the table to show additional options.
4) Click on "Statistics" to display the statistical analysis of the data.
5) In the statistical analysis, look for the correlation coefficient (also known as the Pearson correlation coefficient or r value).
The correlation coefficient ranges between -1 and 1. A value close to 1 indicates a strong positive linear relationship between the two variables, while a value close to -1 indicates a strong negative linear relationship. A value close to 0 indicates a weak or no linear relationship.
Please follow these steps on the Desmos graphing calculator to find the equation of the line of best fit, the expected height after 13 months, and the correlation coefficient.
To find the equation of the line of best fit and answer the questions, you can use the Desmos graphing calculator. Here's how you can do it:
Step 1: Go to the Desmos website (https://www.desmos.com/) or download the Desmos app on your device.
Step 2: Click on the "+ New Graph" button to create a new graph.
Step 3: Enter the data from the table into the calculator. You can do this by clicking on the equation input bar and typing the values in pairs, for example, (1, 2.3), (2, 3.6), (3, 5.2), and so on.
Step 4: Once you have entered all the data points, you can press Enter or click the "+" button to add the points to the graph.
Step 5: Click on the wrench icon at the top right corner of the graphing calculator to access additional options.
Step 6: Under the Statistics section, select "Linear" as the regression type. This will calculate the equation of the line of best fit.
a) The calculator will display the equation of the line of best fit. By examining the trend in the data, you can determine if a linear model is appropriate or if a different model may be more accurate. Once you have the equation, you can substitute 13 for the number of months to estimate the plant's expected height after 13 months.
b) The calculator will also display the correlation coefficient, also known as the Pearson's correlation coefficient (r). This value ranges between -1 and 1, with -1 representing a perfect negative correlation, 1 representing a perfect positive correlation, and 0 indicating no correlation. A correlation coefficient close to -1 or 1 indicates a strong relationship between the variables. The closer the correlation coefficient is to 0, the weaker the relationship. You can use this value as an indicator of how confident you can be in your predicted value.
By using the Desmos graphing calculator and following these steps, you can find the equation of the line of best fit, estimate the plant's expected height after 13 months, and determine the correlation coefficient.
so, did you use Desmos?
There are several other handy linear regression calculators online as well.