1 / 7

3.2 Correlation

Linear relations are important because, when we discuss the relationship between two quantitative variables, a straight line is a simple pattern that is quite common. A strong linear relationship has points that lie close to a straight line.

nikitas
Download Presentation

3.2 Correlation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Linear relations are important because, when we discuss the relationship between two quantitative variables, a straight line is a simple pattern that is quite common. A strong linear relationship has points that lie close to a straight line. A weak linear relationship has points that are widely scattered about a line. 3.2 Correlation

  2. Our eyes are not good measures of how strong a linear relationship is... • A numerical measure along with a graph gives the linear association an exact value.

  3. In words, standardize each value, multiply corresponding standardized values, add them together, and divide by n-1

  4. Let’s calculate r! The paper “A Cross-National Relationship Between Sugar Consumption and Major Depression?” (Depression and Anxiety [2002]:118 – 120) concluded that there was a correlation between refined sugar consumption (calories per person per day) and annual rate of major depression (cases per 100 people) based on data from 6 countries. The following data were read from a graph that appeared in the paper: Compute the correlation coefficient for this data set. Is the correlation positive or negative? Weak, moderate or strong?

  5. Let’s calculate r!

  6. Facts about Correlation • Correlation makes no distinction between explanatory and response variables. • Correlation requires that both variables be quantitative. • r doesn't change when we change the units of measurement of x, y, or both. • r is positive when the association is positive and is negative when the association is negative. • The correlation r is always a number between -1 and 1. Values of r near 0 indicate a very weak linear relationship. The strength of the linear relationship increases as r moves away from 0 toward either -1 or 1. • Correlation measures strength of linear relationships only. • Like mean and standard deviation, the correlation is not resistant. • Correlation is not a complete summary of two-variable data. You should give the means and standard deviations of both x and y along with the correlation.

  7. Patterns closer to a straight line have correlations closer to 1 or -1

More Related