SECTION 3.3
Coefficient of Determination
Coefficient of determination
r = correlationr2 = coefficient of determination
What this means? Tells us the proportion (or percent) of
variability in y that is explained by the LSRL and variation in x.
Coefficient of determination
x 0 3 6y 0 10 2
Coefficient of determination
x y 2
0 0 163 10 366 2 4
Coefficient of determination
x y0 0 16 93 10 36 366 2 4 9
Coefficient of determination
x y0 0 16 93 10 36 366 2 4 9
56 54SST SSE
SST = sum of squares of the deviations
SSE = sum of squares for error
Coefficient of determination
x y0 0 16 93 10 36 366 2 4 9
56 54SST SSE
π2=πππ βπππΈπππ
π2=πππ βπππΈπππ =
56β5456 =0.0357
Coefficient of determination
3.57% of the variation in y is explained by least-squares regression of y on x.
Coefficient of determination
x 0 5 10y 0 7 8
Coefficient of determination
x y 2
0 0 255 7 410 8 9
Coefficient of determination
x y0 0 25 15 7 4 410 8 9 1
Coefficient of determination
x y0 0 25 15 7 4 410 8 9 1
38 6SST SSE
84.2% of the variation in y is explained by least-squares regression of y on x.
Coefficient of determination
Please note:
Comparing r2 Values, Ex. 3.12, p. 162
Distinction between explanatory and response variables is essential.
Please remember
If you are given the percent of variation, you can find the correlation. Same for correlation variation.
Practice Problems
Exercises 3.42, 3.43