Partitioning Sums of Squares

This section discusses the sums of squares, including partitioning sum of squares into sums of squares predicted and sum of squares error.

Answers


  1. To compute a deviation score you subtract the mean. 15 - 10 = 5.

  2. To compute SSY, first compute the deviation scores (y) by subtracting the mean (10) from each number. Then square these values and add them together: (-8)2 + (-1)2 + 12 + 32 + 52 = 100

  3. SSY = SSY' + SSE; SSE = SSY - SSY' = 25.5 - 18.3 = 7.2

  4. Proportion of variation explained = SSY'/SSY, so as SSY' increases, so does the proportion of variation explained.

  5. Proportion explained = SSY'/SSY; SSY' = (.3)(20) = 6

  6. r2 is the proportion of variation explained. (.84)2 = .71