What Do You See?. A scatterplot is a graphic tool used to display the relationship between two quantitative variables. How to Read a Scatterplot A scatterplot.

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Presentation transcript:

What Do You See?

A scatterplot is a graphic tool used to display the relationship between two quantitative variables. How to Read a Scatterplot A scatterplot consists of an X axis (the horizontal axis), a Y axis (the vertical axis), and a series of dots. Each dot on the scatterplot represents one observation from a data set. The position of the dot on the scatterplot represents its X and Y values. Response and explanatory variables – causative or associative relationships

A scatterplot is a graphic tool used to display the relationship between two quantitative variables. How to Read a Scatterplot A scatterplot consists of an X axis (the horizontal axis), a Y axis (the vertical axis), and a series of dots. Each dot on the scatterplot represents one observation from a data set. The position of the dot on the scatterplot represents its X and Y values. Response and explanatory variables – causative or associative relationships

Patterns of Data in Scatterplots Scatterplots are used to analyze patterns in bivariate data. These patterns are described in terms of, direction, outliers, linearity, and strength. (DOLS) Overall

Patterns of Data in Scatterplots Scatterplots are used to analyze patterns in bivariate data. These patterns are described in terms of, direction, outliers, linearity, and strength. (DOLS) Overall

Making a Scatterplot – Homework vs. Tests

Correlation coefficients measure the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient, measures the strength of the linear association between variables.

The sign and the value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables. The value of a correlation coefficient ranges between -1 and 1. The greater the absolute value of a correlation coefficient, the stronger the linear relationship. The strongest linear relationship is indicated by a correlation coefficient of - 1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger. A negative correlation means that if one variable gets bigger, the other variable tends to get smaller. Keep in mind that the Pearson product-moment correlation coefficient only measures linear relationships. Therefore, a correlation of 0 does not mean zero relationship between two variables; rather, it means zero linear relationship. (It is possible for two variables to have zero linear relationship and a strong curvilinear relationship at the same time.)

Several points are evident from the scatterplots. When the slope of the line in the plot is negative, the correlation is negative; and vice versa. The strongest correlations (r = 1.0 and r = -1.0 ) occur when data points fall exactly on a straight line. The correlation becomes weaker as the data points become more scattered. If the data points fall in a random pattern, the correlation is equal to zero. Correlation is affected by outliers. Compare the first scatterplot with the last scatterplot. The single outlier in the last plot greatly reduces the correlation (from 1.00 to 0.71).