1. Research Methodology Lecture No :26 (Hypothesis Testing – Relationship)

2. Recap Null and Alternate hypotheses Choosing the appropriate test based on number of variables and the type of scales Setting criteria for acceptance and rejection (significance level) Group difference

3. Objective Hypothesis testing the relationship/Association Correlations Regression

4. We already know Descriptive versus Inferential Statistics Statistic versus Parameter Continuous(Ratio, Interval) versus Discrete Variables (Nominal, Ordinal) Measures of Central Tendency Measures of Variability Parametric (data normal distribution) Vs. Nonparametric (no need for normal distribution)

5. Measure association Pearson correlation coefficient r symbolized the coefficient's estimate of linear association based on sampling data Correlation coefficients reveal the magnitude and direction of relationships Coefficient’s sign (+ or -) signifies the direction of the relationship Assumptions of r Linearity Bivariate normal distribution

6. Correlations among Variables

7. Regression Inferential statistics Simple Regression – (One independent and One Dependent variable) – Lowering the salary influences the performance Multiple Regressions – When simultaneously multiple independent variables influence the dependent variables – Independent variables jointly are regressed – Need interval or ratio scale to use regression

8. R-Square is the value which indicates that the amount of variance explained on the dependent variable by the independent variable. X  Y Y=f(x) Y=a+bx1+e Here, x is person birth year, while a and b symbolize constants (fixed numbers). These constants are the regression coefficients, or, to be more exact, the a is often called the constant or the intercept

9. while the b is called variable x’s regression coefficient because it determines how the predicted y values change as the value of x changes. The value of R-Square is between 0 and 1 Say we receive R-Square value.11 and sign level is 0.099 and standard error is 0.80 constant is 0.04

10. It means that 11 percent of variance in the dependent variable is explained by the independent variable and the chances of it not to be true is 9 to 10 percent. In case there are multiple independent variables then we need to see their separate contribution

11. Multi Regression

13. Stepwise Multi Regression

14. The independent variables are customer perceptions of 1) cost/speed valuation, 2) security, and 3) reliability. In model 3, reliability is added. Looking at the R2 column, you can see that the cost/speed variable explains 77% of customer usage.

15. The adjusted R2 for model 3 is.871. R2 is adjusted to reflect the model’s goodness of fit for the population. The standard error of model 3 is.4937.

16. Unstandardized regression coefficients for all three models are shown in the lower table in the column headed B. The equation can be constructed as Y= -.093 +.448X1 +.315X2 +.254X3+0.497

17. Standardized regression coefficients are shown in the column labeled Beta. Standard error is a measure of the sampling variability of each regression coefficient.

18. Examples A study in behavior consider many variables influencing the an individual intentions The researcher is interested to test the role of attitude, subjective norms and perceived behavior control. They theorize the model as attitude, subjective norms and perceived behavior control effects the intentions.

19. They also hypothesize that attitude influence the intentions in positive manner. They hypothesize that subject norms have positive effect on intentions. They also hypothesize that perceived intentions control effects the behavior in positive way.

20. They also hypothesize that attitude, subjective norms, perceived behavior control will significantly explain the variability in the intentions Attitude, subjective norm and Perceived Behavior control effect the intnetions of the individual. Model equation: Int=f(Att,Pbc,SN)

21. The correlations between the different variables are

23. SPSS and Regression