R Squared.

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Presentation transcript:

R Squared

r = -.944

r = -.79

Which value for Y is a more accurate prediction for the given X value? y = -0.9402x + 43.721 y = -0.8141x + 9.1332 if x = 15, y = ? if x = 6, y = ? y = -0.9402(15) + 43.721 y = -0.8141(6) + 9.1332 y = 29.6195 y = 4.2486 Which value for Y is a more accurate prediction for the given X value?

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 actual Y values and their mean

For example, here’s how to find the R Squared value for the data/graph below: X Y 3 40 10 35 11 30 15 32 22 19 26 23 24 28 18 6 Equation for Line of Best Fit: y = .94x + 43.7 Correlation = -.94

Equation for Line of Best Fit: y = .94x + 43.7 Predicted Y Value Error Error Squared Distance between Y values and their mean Mean distances squared 3 40 10 35 11 30 15 32 22 19 26 23 24 28 18 6 Mean: Sum:

Equation for Line of Best Fit: y = .94x + 43.7 Predicted Y Value Error Error Squared Distance between Y values and their mean Mean distances squared 3 40 40.88 .88 .77 14.8 219.04 10 35 34.30 -.70 .49 9.8 96.04 11 30 33.36 3.36 11.29 4.8 23.04 15 32 29.60 -2.40 5.76 6.8 46.24 22 19 23.02 4.02 16.16 -6.2 38.44 26 -2.98 8.88 .8 .64 23 24 22.08 -1.92 3.69 -1.2 1.44 28 17.38 -4.62 21.34 -3.2 10.24 18 -.62 .38 -7.2 51.84 6 10.80 -19.2 368.65 Mean: 25.2 Sum: 91.81 855.60

1- 1- 1- 0.11 =.89 91.81 855.60 To calculate “R Squared”… Sum of squared distances between the actual and predicted Y values actual Y values and their mean 1- 91.81 855.60 1- 0.11 =.89

The value we got for R Squared was .89 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 X Y 3 40 10 35 11 30 15 32 22 19 26 23 24 28 18 6 r = -.944 r2 = -.944 • -.944 r2 = .89

R Squared To determine how well the regression line fits the data, we find a value called R-Squared (r2) To find r2, simply square the correlation The closer r2 is +1, the better the line fits the data r2 will always be a positive number

r = -.944 r2 = .89

r = -.79 r2 = .62