the table shows the height of a plant at each month. Use the table to answer the questions.
number of months | height of plant (in)
1 | 2.3
2 | 3.6
3 | 5.2
4 | 4.9
5 | 7.3
6 | 7.6
7 | 8.0
a) What is the equation of the line of best fit?
b) How tall can we expect the plant to be after 13 months?
a) To find the equation of the line of best fit, we can use linear regression. Using the given data points:
Number of months (x): 1, 2, 3, 4, 5, 6, 7
Height of plant (y): 2.3, 3.6, 5.2, 4.9, 7.3, 7.6, 8.0
We can plug these values into a graphing calculator or statistical software to find the equation of the line of best fit. Assuming the line is in the form y = mx + b (where m is the slope and b is the y-intercept), the equation is:
y = 0.946x + 1.286
b) To find the height of the plant after 13 months, we can plug in 13 for x in the equation of the line:
y = 0.946(13) + 1.286
y = 12.318 + 1.286
y ≈ 13.604
Therefore, we can expect the plant to be approximately 13.604 inches tall after 13 months.
c) What is the correlation coefficient? How confident can you be that your predicted value will be reasonably close to the actual value?
To determine the correlation coefficient, we can use statistical software or a graphing calculator. The correlation coefficient, also known as r, measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient measures the relationship between the number of months and the height of the plant.
For the given data points:
Number of months (x): 1, 2, 3, 4, 5, 6, 7
Height of plant (y): 2.3, 3.6, 5.2, 4.9, 7.3, 7.6, 8.0
The correlation coefficient is approximately 0.940. The correlation coefficient ranges from -1 to 1, where -1 indicates a strong negative relationship, 1 indicates a strong positive relationship, and 0 indicates no relationship.
In this case, a positive correlation close to 1 suggests that there is a strong positive relationship between the number of months and the height of the plant. This means that as the number of months increases, the height of the plant also tends to increase.
Based on the high correlation coefficient of 0.940, we can be reasonably confident that our predicted value of 13.604 inches after 13 months will be reasonably close to the actual value. However, it is important to note that there may still be some variation or uncertainty in the prediction.