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Published byMicah Alltop Modified about 1 year ago

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R Squared

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r = -.944

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r = -.79

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y = x y = x if x = 15, y = ? y = (15) y = if x = 6, y = ? y = (6) y = Which value for Y is a more accurate prediction for the given X value?

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To find how well the Line of Best Fit actually fits the data, we can find a number called R-Squared by using the following formula: 1- Sum of squared distances between the actual and predicted Y values Sum of squared distances between the actual Y values and their mean

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XY Equation for Line of Best Fit:y =.94x Correlation = -.94 For example, here’s how to find the R Squared value for the data/graph below:

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XY Predicted Y Value Error Error Squared Distance between Y values and their mean Mean distances squared Mean:Sum: Equation for Line of Best Fit:y =.94x

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XY Predicted Y Value Error Error Squared Distance between Y values and their mean Mean distances squared Mean:25.2Sum:91.81Sum: Equation for Line of Best Fit:y =.94x

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1- Sum of squared distances between the actual and predicted Y values Sum of squared distances between the actual Y values and their mean To calculate “R Squared”… =.89

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XY r = OK. Don’t kill me. Remember this was the data/graph we were finding “R Squared” for? The value we got for R Squared was.89 Here’s a short-cut. To find R Squared… …Square r r 2 = r 2 =.89

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R Squared To determine how well the regression line fits the data, we find a value called R-Squared (r 2 ) To find r 2, simply square the correlation The closer r 2 is +1, the better the line fits the data r 2 will always be a positive number

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r = r 2 =.89

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r = -.79 r 2 =.62

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