31
Bivariate Analysis
� Correlations :
Positive
Negative
where r is the correlation coefficient
Strong 0.75 �r
� 1
Moderate 0.5 �r
� 0.75
Weak 0 �r
� 0.5
No r � 0
Weak �0.5 � r � 0
Moderate �0.75 � r � � 0.5
Strong �1� r � � 0.75
� Correlation Coefficient for ranked data : r s
: Spearman ’ s Rank Correlation Coefficient
� Coefficient of determination :
2
R : Coefficient of determination
2
R % of the variability of the data can be explained by the regression model
� Sum of square residuals : x x
1 x
2
… x n y y
1 y
2
… y n
Predicted value of y n
1 SS � ( y �yˆ
)
�
res i i n i � 1
� Non-linear regressions :
1 . Quadratic regression 2 . Cubic regression 3 . Quartic regression 4 . Exponential regression 5 . Logarithmic regression 6 . Power regression
7 . Logistic regression
2 ŷ
1 ŷ
2
… y ˆn
: Sum of square residuals
www . seprodstore . com
33