The table shows the height of a plant at each month. Use the table to answer the questions ( use the demos graphing calculator to do this problem)
Numbers 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 fits? How tall can we expect the plant to be after 13 months?
b). What is the correlation coefficient? How confident can you bc your predicted value will be reasonably close to the actual value?
To find the equation of the line of best fit and predict the plant's height after 13 months, we can use a graphing calculator.
a) Equation of the line of best fit:
1. Go to the Desmos graphing calculator website (https://www.desmos.com/calculator).
2. Click on the "+" button in the top left corner to create a new graph.
3. In the expression input box, type the month numbers in a list, and the corresponding plant heights in a second list. For this problem, you would enter (1,2.3), (2,3.6), (3,5.2), (4,4.9), (5,7.3), (6,7.6), (7,8.0) in the lists.
4. Once you have entered the data, the graphing calculator will automatically create a scatterplot of the points.
5. To fit a line to the data, click on the "+" button next to the equation list and choose the "Line" option.
6. The equation of the line of best fit will be displayed on the graph.
To predict the plant's height after 13 months:
1. On the same graph, enter the value 13 in the expression input box for the months.
2. The calculator will automatically calculate the estimated height of the plant after 13 months based on the line of best fit, which will be displayed on the graph.
b) Correlation coefficient and prediction accuracy:
1. Look at the graph and find the correlation coefficient value, which should be displayed near the line of best fit. The correlation coefficient measures the strength and direction of the linear relationship between the two variables (months and plant height).
2. A correlation coefficient value close to 1 indicates a strong positive linear relationship, which means the predicted value is likely to be reasonably close to the actual value.
3. However, it's important to note that correlation does not imply causation, so other factors may also influence a plant's growth.
Using the Desmos graphing calculator, you can find the equation of the line of best fit and predict the plant's height after 13 months, as well as determine the correlation coefficient and assess the confidence level of your prediction.