Introduction to Statistics course :

here is the question

1-Partitioning Sums of Squares

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Partitioning the Sums of Squares Learning Objectives 1. Compute the sum of squares Y 2. Convert raw scores to deviation scores 3. Compute predicted scores from a regression equation 4. Partition sum of squares Y into sum of squares predicted and sum of squares error 5. Dene r2 in terms of sum of squares explained and sum of squares Y One useful aspect of regression is that it can divide the variation in Y into two parts: the variation of the predicted scores and the variation in the errors of prediction. The variation of Y is called the sum of squares Y and is dened as the sum of the squared deviations of Y from the mean of Y. In the population. the formula is SSY = 20' no: where SSY is the sum of squares Y. Y is an individual value of Y, and my is the mean of Y. A simple example is given in Table l . The mean on is 2.06 and SSY is the sum of the values in the third column and is equal to 4.597. Table 1. Example of SSY. When computed in a sample. you should use the sample mean, M, in place of the population mean: ssr = 20' My)2 it is sometimes convenient to use formulas that use deviation scores rather than raw scores. Deviation scores are simply deviations from the mean. By convention. small letters rather than capitals are used for deviation scores. Therefore. the score, y indicates the difference between Y and the mean of Y. Table 2 shows the use of this notation. The numbers are the same as in Table I . Table 2. Example of SSY using Deviation Scores. The data in Table 3 are reproduced from the introductory section. The column X has the values of the predictor variable and the column '1' has the criterion variable. The third column, y, contains the the differences between the column Y and the mean of Y