Page 159 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

2
amount of total sum of squares (∑y ) that can be explained in
regression model. It is one the portion of total sum of square.
2
Residual sum of square = SS res=∑ (Y - Y') = 90.15561
SS res the amount of variance in a data set that is not defined by the
regression model. The SS res = 90.15561 is the measurement of error
remaining between regression function and data set. Residual sum
of square or ‘unexplained sum of square’ is again the amount of
2
total sum of squares (∑y ) that can be explained in regression
model.
Therefore it can be said defined that:
2
̅
2
∑y =∑ (Y - Y') + ∑ (Y' - ) 2
2
Or ∑y =SS res+SS reg
Or Total sum of square = Sum of square explained +
sum of square unexplained

F ratio in the problem #1 is 14.9422 with 1 and 18 df (degree of
freedom). For example, the significance level α=0.05, it is found in
the F table with 1 and 18 df is 4.41. As obtained F is greater than
tabulated value, it is concluded that the regression Y on X is
statistically significant.

The Theory and Applications of Statistical Inferences 143