NYC Charter School Performance on the 2012-13 State Exams
1. Bivariate Correlations
2. Linear Regression Analysis
3. Multiple Regression Analysis
Bivariate Correlations
Bivariate Correlation
Paersone Correlation or Co-efficient of correlation
Scale level of measurement
p<0.05 Significant Correlation
Researcher can be 95% confident that the relationship between these two variables is not due to chance
Denoted by r
-1 ≤ r ≤ +1 0 ------- ±0.3 No Relation
±0.3 ------- ±0.5 Weak Relation
±0.5 ------- ±0.8 Moderate Relation
±0.8 ------- ±1 Strong Relation
1 is total positive correlation, 0 is no correlation, and −1 is negative correlation
The closer the value is to -1 or +1, the stronger the association is between the variables
Linear Regression Analysis
Outlier There should be no significant outliers. Outliers are simply
single data points within your data that do not follow the usual pattern.
The problem with outliers is that they can have a negative effect on the regression equation that is used to predict the value of the dependent (outcome) variable based on the independent (predictor) variable.
Multiple Regression: Model Suma. R tells the reliability & mathematical relationship.1. R Square (co-efficient of determination) tells the
percentage of accuracy.2. Also percentage of variation that can not be controlled i.e.3. (1-R Square)i. Adjusted R2, It can be negative & always less than or
equal to Rii. Adjusted R2 will be more useful only if the R2 is
calculated based on a sample, not the entire populationiii. Adjusted R2 increases only if the new term improves the
model more than would be expected by chance
ANOVA ANOVA table tests whether the overall regression
model is a good fit for the data. p<0.05 The table shows that the independent variables
statistically significantly predict the dependent variable, F(3, 16) = 32.811, p < .0005 (i.e., the regression model is a good fit of the data)
Coefficients
How much the dependent variable varies with an independent variable , when all other independent variables are held constant.
T value less than ±2 is not important Significant value of x
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