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But, how reliable will these prediction be? It would seem that the closer the scatter plots are to the best fit line, the more reliable the predictions from the regression equation.
Is there a way to determine how well our regression equation fits our data? There is a way of measuring the "goodness of fit" of the best fit line least squares linecalled the correlation coefficient. It is a number between -1 and 1, inclusive, which indicates the measure of linear association between the two variables, and also shows whether the correlation is positive or negative.
A correlation greater than 0.
These values can vary based upon the "type" of data being examined. A study utilizing scientific data may require a stronger correlation than a study using social science data.
NOTE: Comparing correlation coefficients of different regression models for the same set of data should not be used to determine which is the "best" regression model. If not, you will not see the r-value. When you choose a regression equation on the calculator, the correlation coefficient will be displayed on the screen with the regression equation correlation coefficient trend line assuming the Diagnostics are turned on.
Scatter Plots and Trend Lines Day 3: Correlation Coefficients
The linear regression screen shown at the right shows an "r" value of 0. The linear regression equation, in this case, will be a reliable model for future forecasts or predictions.
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For calculator correlation coefficient trend line with.