Explained Variance

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Explained Var. Ans.

You can link to an explained variance applet that demonstrates how changes in the configuration of the scatterplot affect the amount of explained and unexplained variance, and the value of the correlation coefficient.

• Read Instructions (printing a hard copy, if possible, for easy reference.)
• To automatically generate a continuous cycle of small changes in input, check one of the "animate" buttons, for example, that for the standard error of estimate (SE), and note the effect of these input changes on the scatterplot, the value of the r, and the amount of explained and unexplained variance.
• After the first cycle of small input changes, reset to the original inputs and configuration by clicking on "Done" then "Begin". Start a new cycle by checking, one at a time, each of the two remaining "animate" buttons.
• Click on "Begin" to start demonstration, and when finished answer the questions below.

Questions:

1. What happens to the value of the correlation coefficient and also, just a square away, the proportion of explained variance – that is, most generally, what happens to the degree of predictability -- as the value of the standard error of estimate increases?  Answer

2. What happens to the degree of predictability as the value of the slope, whether positive or negative, approaches zero?  Answer

3. What happens to the degree of predictability with decreases in the value of the standard deviation of X?  Answer