Page 182 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

indicates correlation between x 1 and x 2. Since r 12 is positive and less
than 0.2, it can be concluded that x1 and x2 has a weak positive
correlation. (r y1=0.6735) indicates correlation between y and x 1.
Since r y1 is positive and greater than 0.5, it can be concluded that y
and x 1 has a positive moderate correlation. (r y2=0.5320) indicates
correlation between y and x 2. Since r y2 is positive and greater than
0.5, it can be concluded that y and x 2 has a positive moderate
correlation. Sum of square regression (SS reg=106.661) is analysis of
variance, it is also known as sum of square explained. On the other
hand sum of square residuals (SS res=58.3398) is the difference
between the total sum of square and sum of square explained. In
2
this problem, the overall correlation R y. 12 =0.6464, which indicates
that the overall variables have a positive correlation. F ratio in the
problem #1 is 15.54 with 1 and 17 df (degree of freedom). For
example, the significance level α=0.05, it is found in the F table with
1 and 17 df is 4.45. As obtained F is greater than tabulated value, it
is concluded that the regression Y on X is statistically significant. The
calculated F(1,17) = 9.27 while the critical value of F(1,17) is 4.45, so
F for the increment of X 2 over X 1 is significant. The calculated F(1,17)
= 17.47 while the critical value of F(1,17) is 4.45, so F for the
increment of X 1 over X 2 is quite significant.

The Theory and Applications of Statistical Inferences 166