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Correlation & Linear Regression
Explanation of Correlation: Interactive Animation
Correlation is Prediction: Lecture Tool
Correlation is "Shared" Variance: Interactive Animation
Illustrated Calculations: Calculation of Regression & Correlation Values
Glossary of Regression & Correlation Terms
Example Values: Values from Illustrated Calculations

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### #### [click here for video]Correlation tells how much I can reduce prediction error

The user selects the sample size and population correlation value. The software generates a data set from that population and plots the values. All the "Display Options" of the plot are shown. The red bar represents the mean value of Y ± 1 standard deviation. The purple bar represents the predicted value ± 1 standard error of estimate. The user can drag the arrow (just below the X-axis) to sweep across the display. Two-thirds of the observations should be within both the red and purple bars. The degree of correlation is shown by the degree to which the purple bar is shorter than the red bar.

### #### Is Haircolor correlated with weight?

This is a classroom exercise. Students make predictions of a man's weight based on 4 clues (he is a man, he has brown hair, he is 6'2" tall, he plays lineman on a football team). In the final step, the man's weight is revealed and the absolute errors are displayed. An uncorrelated variable (hair color) doesn't reduce prediction error. A correlated variable (height) does.

### #### Total Variance less Shared Variance

Dragging the blue circle on the left changes the amount of overlap with the green and recalculates the correlation and associated values.

The larger the yellow area, the less green area and the less the Y scores can "vary". This means better predictions.

### What does the calculator do?

The values for the correlation coefficient and linear regression calculated for a data set pasted onto the card.

The data set can be generated in the "Bivariate Data Simulation" card, copied, and then pasted here.

### #### How do you say...

This is the static page that opens when the red "info" button on the "Correlation & Regression Tutor" is clicked.

The various terms and notations are described.

Clicking the "Numeric Example" arrow, goes to the next screen.

### The values are ...

This card combines the values for the current data set with the notation introduced on the Glossary of Terms card to assure the student is connecting the values with the notation and the meaning.