A P STATISTICS LESSON 3 – 2 CORRELATION

ESSENTIAL QUESTION: What is the Correlation Coefficient, characteristics and how is it used to analyze data? To find the Correlation Coefficient of Data. To find out what its characteristics. To find out how The Correlation Coefficient can be used to analyze data.

Correlation r The correlation measures the direction and strength of the linear relationship between two quantitative variables. Correlation is usually written as r. Suppose that we have data on variables x and y for n individuals. The values for the first individual are x1 and y1, the values for the second individual x2 and y2, and so on. The means and standard deviations of the two variables are x and sx for the x-axis and y and sy for the y-axis. The correlation r between x and y is ¯ ¯

Correlation

Facts about Correlation Correlation makes no distinction between explanatory and response variables. It makes no difference which variable you can call x and which you call y in calculating the correlation. Correlation requires that both variables be quantitative, so that it makes sense to do the arithmetic by the formula for r. Because r uses the standardized values of the observations , r does not change when we change the units of measure of x, y, or both.

Fact about Correlation (continued…) Positive r indicates positive association between two variables and negative r indicates negative association. The correlation r is always a number between -1 and 1. Correlation measures the strength of only a linear relationship between two variables. Like the mean and standard deviation, the correlation is not resistant: r is strongly affected by a few outlying observations.

Correlation and the Calculator You can easily have the TI-83/84 compute the value of r given a list. **Before you compute a regression model, press 2nd 0 (catalog), scroll down to DiagnosticOn, select it, and press enter until you see Done. You have turned on additional features with regards to regression. NOW you can see r as part of the output screen when you calculate linear regression!