# Correlation & linear regression

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Information about Correlation & linear regression
Education

Published on March 10, 2014

Source: slideshare.net

## Description

Topic: Correlation & Linear regression
Subject: QTIA
Software: SPSS
Dr Faisal Afzal Siddiqui

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 ------- ±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 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

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