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The correlation coefficient is commonly used in various scientific disciplines to quantify an observed relationship between two variables and communicate the strength and nature of the relationship. This vignette will help build a student's understanding of correlation coefficients and how two sets of measurements may vary together.
Significant figures are used in everyday measurements, where accurate values are needed to provide concise quantitative answers. Measuring devices such as rulers, calculators or thermometers all have limits to their precision, thus all numerical values are only as accurate as the measurement tool used to collect the data. This vignette will reinforce or establish a student's understanding of significant figures and how the "Atlantic-Pacific Rule" (Stone 1989) can be applied for any given measurement or mathematical operation.
Normal Distribution is one of the fundamental probability distributions used in statistics to predict the outcomes for a set of measurements, such as the overall height of a population and is commonly known as the bell curve or Gaussian distribution. Thus, the normal distribution shows the behavior of the variable by listing all possible observed outcomes based on available data. The vignette will reinforce or establish a student's understanding of Normal Distribution, the parameters that facilitate the size and shape of the distribution (mean and standard deviation), and how it is applied to express probable outcomes and outliers for an event. The concept will be reviewed by analyzing the probability distribution for pizza delivery times and demonstrating it in a following exercise.
Linear Regression is similar to the correlation coefficient in that both are utilized to understand the relationship between two sets of measurements. Regression expands this concept to create modeled predictions from the extension of the best fit line between a dependent and independent variable. This vignette will help build a student's understanding of linear regression and how to interpret R2 coefficients by analyzing lines of best fit.