Curve of Best Fit Analysis
A Grade 12 Math worksheet focusing on understanding and applying the curve of best fit, including linear, quadratic, and exponential regressions.
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Curve of Best Fit Analysis
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Read each question carefully and provide the best answer. Show all your work for short answer questions. Use a graphing calculator where appropriate.
1. Which of the following is the primary purpose of finding a curve of best fit?
To connect all the data points perfectly.
To predict future values or understand relationships between variables.
To calculate the mean of the data set.
To identify outliers without further analysis.
2. A scatter plot shows a general upward trend, but the rate of increase appears to be slowing down. Which type of curve of best fit would be most appropriate?
Linear
Quadratic
Exponential
Logarithmic
1. The coefficient of determination, denoted by R², measures the proportion of the in the dependent variable that is predictable from the independent variable(s).
2. When extrapolating beyond the range of the given data, the predictions made by the curve of best fit become less .
1. A researcher collects data on the number of hours students study (x) and their exam scores (y). The linear regression equation is found to be y = 5x + 60. Interpret the slope and the y-intercept in the context of this problem.
The following data represents the growth of a plant (in cm) over several weeks:
Week (x)
Height (y)
1
2.5
2
5.8
3
10.1
4
15.7
5
22.0
1. Plot the data on the coordinate plane below. Label your axes.
2. Based on the scatter plot, what type of curve of best fit (linear, quadratic, or exponential) do you think would be most appropriate for this data? Justify your answer.
1. A high correlation coefficient (close to 1 or -1) always implies causation between the variables.
True
False