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# Dependance Technique, Regression & Correlation

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### Dependance Technique, Regression & Correlation

1. 1. Dependence Technique, Regression and correlation , standard multiple regression Presented By Ms. Qurat-ul-Ain Salman Asmat M. Usman Ahmed 1
2. 2. Content of Presentation o Dependence Techniques 1. Correlation 2. Regression Simple Regression Multiple Regression Standard Multiple Regression o Demonstration and Interpretation 2
3. 3. Dependence Technique It is a statistical technique distinguished by having a variable or a set of variables identified as dependent variable(s) and remaining variables as independent vaiables.The object of Dependence technique is the prediction of dependent variables by the independent variables. Or in simple words dependence technique is in which variables are easily classified as dependent and independent variables. Examples are correlation and regression analysis 3
4. 4. Correlation  Correlation is the average relationship between two or more variables.  It represents with r  It lies between +1 to -1  When variables are dependent on time than correlation is applied  +1 indicates +ve correlation  -1 indicates –ve correlation  Zero correlation indicates no relationship 4
5. 5. Types of correlation.  Positive correlation  Negative correlation  Perfectly positive  Perfectly negative  Zero correlation  Linear correlation 5
6. 6. Positive correlation  When two variables moves in the same direction then correlation between two variables are said o be positive  When the value of one variable increase ,the value of other variable also increases at the same rate Example: Training and performance of employees in the company 6
7. 7. Negative correlation  Two variables moved in the opposite direction when value of variable increases the value of other variable decreases example: The relationship between price and demand 7
8. 8. Perfect positive correlation  When there is a change in one variable, and if there is equal proportion of change in the other variable in the same direction then these two variables said to be in perfectly positive correlation 8
9. 9. Types  Perfectly negative correlation: Between two variables X and Y if the change in X causes the same amount of change in Y in equal pro portion but in opposite direction.  Zero correlation: When two variables are independent and the change in one variable has no effect in other variable 9
10. 10. Types  Linear correlation: If the quantum change in one variable has the ratio of change is the quantum of change in other variable is known as linear correlation 10
11. 11. Methods of determine correlation Following are the methods of determine the correlation  Scatter plots  Karl Pearson’s coefficient of correlation  Spearman’s rank correlation 11
12. 12. Regression Analysis  Regression analysis is the generic term for several statistical tests for evaluating the relationship between interval level dependent and independent variables.  When we are considering the relationship between one dependent variable and one independent variable, we use Simple Linear Regression.  When we are considering the relationship between one dependent variable and more than one independent variable, we use Multiple Regression.  SPSS uses the same procedure for both Simple Linear Regression and Multiple Regression, which adds some complications to our interpretation. 12
13. 13. Purpose of Simple Linear Regression  The purpose of simple linear regression analysis is to answer three questions that have been identified as requirements for understanding the relationship between an independent and a dependent variable:  Is there a relationship between the two variables?  How strong is the relationship (e.g. trivial, weak, or strong; how much does it reduce error)?  What is the direction of the relationship (high scores are predictive of high or low scores)? 13
14. 14. Example of simple linear Regression  There is a relationship between undergraduate GPA’s and graduate GPA’s.  GRE scores are a useful predictor of graduate GPA’s.  For social work students, the relationship between GPA and future income enables us to predict future earnings based on academic performance. 14
15. 15. The Regression Equation The regression equation is the algebraic formula for the regression line, which states the mathematical relationship between the independent and the dependent variable. We can use the regression line to estimate the value of the dependent variable for any value of the independent variable. The stronger the relationship between the independent and dependent variables, the closer these estimates will come to the actual score that each case had on the dependent variable. 15
16. 16. Simple Linear Regression: Hypotheses  The hypothesis tested in simple linear regression is based on the slope or angle of the regression line.  Hypotheses:  Null: the slope of the regression line as measured by the b coefficient = 0, i.e. there is no relationship  Research: the slope of the regression line as measured by the b coefficient ≠ 0, i.e. there is a relationship  Decision:  Reject null hypothesis if pSPSS ≤ alpha 16
17. 17. Standard Regression Equation  The standard form for the regression equation or formula is: Y = a + bX  where  Y is the estimated score for the dependent variable  X is the score for the independent variable  b is the slope of the regression line, or the multiplier of X  a is the intercept, or the point on the vertical axis where the regression line crosses the vertical y-axis 17
18. 18. Purpose of Multiple Regression  The purpose of multiple regression is to analyze the relationship between metric independent variables and a metric dependent variable.  If there is a relationship, using the information in the independent variables will improve our accuracy in predicting values for the dependent variable. 18
19. 19. interpretation  The last column shows the goodness of fit of the model. The lower this number, the better the fit. Typically, if “Sig” is greater than 0.05, we conclude that our model could not fit the data. 19
20. 20. R-square:  Measures the proportion of the variation in the dependent variable (wage) that was explained by variations in the independent variables. In this example, the "R-Square"' tells us that 51% of the variation (and not the variance) was explained. 20
21. 21. Adjusted R-square:  Measures the proportion of the variance in the dependent variable (wage) that was explained by variations in the independent variables. In this example, the “Adjusted R Square” shows that 50.9% of the variance was explained. 21
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24. 24. Applying test 24
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26. 26. Types of Multiple Regression  Standard multiple regression  Hierarchical multiple regression  Stepwise multiple regression 26
27. 27. Standard Multiple Regression • Standard multiple regression is used to evaluate the relationships between a set of independent variables and a dependent variable. • In standard multiple regression, all of the independent variables are entered into the regression equation at the same time 27