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

𝑟2=𝑆𝑆𝑇 −𝑆𝑆𝐸𝑆𝑆𝑇

𝑟2=𝑆𝑆𝑇 −𝑆𝑆𝐸𝑆𝑆𝑇 =

56−5456 =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