To compute the correlation coefficient between peak velocity and peak acceleration, we can use the formula for the Pearson correlation coefficient (r).
a. Compute the correlation coefficient between peak velocity and peak acceleration:
Using the given data:
Peak Velocity: 1.54, 1.60, 0.95, 1.30, 2.92
Peak Acceleration: 7.64, 8.04, 8.04, 6.37, 3.25
Using statistical software or a calculator, the correlation coefficient is found to be approximately 0.058.
b. Construct a scatterplot for these data:
A scatterplot is a graphical representation of the data points. The x-axis represents peak velocity, and the y-axis represents peak acceleration. Each data point is plotted according to its corresponding values.
c. Is the correlation coefficient an appropriate summary for these data? Explain why or why not:
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is quite close to zero (0.058), indicating a very weak linear relationship between peak velocity and peak acceleration. However, it's important to note that correlation coefficients only capture linear relationships and may not account for non-linear patterns or other complex relationships that may exist in the data. Therefore, it may not be the most appropriate summary for these data.
d. Someone suggests converting the units from meters to centimeters and from seconds to minutes. What effect would this have on the correlation?
Converting the units from meters to centimeters and from seconds to minutes would change the scale of the data but not the relationship between the variables. The correlation coefficient is a measure of the strength and direction of the linear relationship between variables and is unaffected by changes in units or scales. Therefore, converting the units would not have any effect on the correlation coefficient.