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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
 -1

by r

 r  +1



0 ------- 賊0.3

No Relation



賊0.3 ------- 賊0.5

Weak Relation



賊0.5 ------- 賊0.8

Moderate Relation



賊0.8 ------- 賊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
Correlation & Linear Regression
Correlation & Linear Regression
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 Sum

a. 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 R
ii. Adjusted R2 will be more useful only if the R2 is calculated based on
a sample, not the entire population
iii. 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
 = 11.823 + 0.5511 + 0.1042 + 1.9893
 How much the dependent variable varies with an
independent variable , when all other independent
variables are held constant.
 T value less than 賊2 is not important
 Significant value of x
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Correlation & Linear Regression

  • 1. NYC Charter School Performance on the 2012-13 State Exams 1. Bivariate Correlations 2. Linear Regression Analysis 3. Multiple Regression Analysis
  • 2. Bivariate Correlations Bivariate Correlation Paersone Correlation or Co-efficient of correlation Scale level of measurement
  • 3. p<0.05 Significant Correlation Researcher can be 95% confident that the relationship between these two variables is not due to chance
  • 4. Denoted -1 by r r +1 0 ------- 賊0.3 No Relation 賊0.3 ------- 賊0.5 Weak Relation 賊0.5 ------- 賊0.8 Moderate Relation 賊0.8 ------- 賊1 Strong Relation
  • 5. 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
  • 9. 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.
  • 10. Multiple Regression: Model Sum a. 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 R ii. Adjusted R2 will be more useful only if the R2 is calculated based on a sample, not the entire population iii. Adjusted R2 increases only if the new term improves the model more than would be expected by chance
  • 11. 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)
  • 12. Coefficients = 11.823 + 0.5511 + 0.1042 + 1.9893 How much the dependent variable varies with an independent variable , when all other independent variables are held constant. T value less than 賊2 is not important Significant value of x