Correlation analysis helps us describe how two numeric variables relate to one another. This lesson introduces paired data and scatter plots, which provide a visual first step in examining a possible relationship.
Bivariate data consists of observations on two variables, with each value for one variable paired with a corresponding value for the other. For example, a finance analyst might pair each month's S&P 500 value with the Nike stock price recorded for that month.
All flashcards
What does Pearson's sample correlation coefficient r measure?
The direction and strength of the linear association between paired numerical variables in a sample.
What is the difference between an explanatory and a response variable?
The explanatory variable is used to help explain or predict the response variable; these roles do not establish causation.
Why must paired values stay together when calculating ∑xy?
Each product must use values from the same observation; mixing pairs changes the data.
What does statistical significance of a correlation test indicate?
Sufficient evidence that the population correlation differs from zero, not proof of causation or practical importance.
Why inspect a scatter plot alongside a correlation coefficient?
The plot can reveal curvature or influential outliers that may make a linear summary misleading.
Quiz questions
Which range must contain the sample correlation coefficient r?Answer: From −1 to 1, inclusive.
What does r=−1 mean for a sample of paired observations?Answer: Every point lies exactly on a line with negative slope.
If a sample has r=0, which conclusion is justified?Answer: The sample has no linear association, though a nonlinear relationship may exist.
What does a statistically significant correlation establish about practical importance?Answer: Significance alone does not establish that the association is practically important.
Why can prediction from a fitted line be unreliable beyond the observed x-values?Answer: It requires extrapolation beyond the range covered by the data.
Based on Principles of Finance by Julie Dahlquist, Rainford Knight (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.