Coefficient of Determination SECTION 3 3 Coefficient of

Coefficient of Determination SECTION 3. 3

Coefficient of determination �r = correlation �r 2 = 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 6 y 0 10 2

Coefficient of determination x y 0 0 16 3 10 36 6 2 4

Coefficient of determination x y 0 0 16 9 3 10 36 36 6 2 4 9

Coefficient of determination x y 0 0 16 9 3 10 36 36 6 2 4 9 56 54 SST SSE SST = sum of squares of the deviations SSE = sum of squares for error

Coefficient of determination x y 0 0 16 9 3 10 36 36 6 2 4 9 56 54 SST SSE

Coefficient of determination �

Coefficient of determination x 0 5 10 y 0 7 8

Coefficient of determination x y 0 0 25 5 7 4 10 8 9

Coefficient of determination x y 0 0 25 1 5 7 4 4 10 8 9 1

Coefficient of determination x y 0 0 25 1 5 7 4 4 10 8 9 1 38 6 SST SSE 84. 2% of the variation in y is explained by least-squares regression of y on x.

Coefficient of determination Please note:

Comparing r 2 Values, Ex. 3. 12, p. 162 Distinction between explanatory and response variables is essential.

Please remember �

Practice Problems �Exercises 3. 42, 3. 43