Correlation & Linear Regression in SPSS

Átírás

1 Correlation & Linear Regression in SPSS

2 Types of dependence association between two nominal data mixed between a nominal and a ratio data correlation among ratio data

3 Exercise 1 - Correlation File / Open / Employee data.sav Is there any relation between - current salary & - beginning salary? CORRELATION

4 Analyze / Correlate / Bivariate 0 I r I 0,3 weak dependence 0,3 I r I 0,7 medium-strong dependence 0,7 I r I 1 strong dependence r Shows direction and strength C Just direction! + -

5 Output Mean Std. Deviation N Current Salary $34, $17, Beginning Salary $17, $7, Current Salary Beginning Salary Current Salary Beginning Salary Pearson Correlation 1,880(**) Sig. (2-tailed),000 Sum of Squares and Cross-products , ,73 Covariance , ,27 N Pearson Correlation,880(**) 1 Sig. (2-tailed),000 Sum of Squares and Cross-products , ,45 Covariance , ,96 N

6 Exercise 2 Multiple Correlation Is there any relation between the current salary previous experience (month) month since hire beginning salary? MULTIPLE CORRELATION

7 Analyze / Correlate / Bivariate r Shows direction and strength 0 I r I 0,3 weak dependence 0,3 I r I 0,7 medium-strong dependence 0,7 I r I 1 strong dependence C Just direction! + -

8 Output View Inverse relationship & weak dependence Direct relationship & strong dependence Current Salary Previous Experience (months) Months since Hire Beginning Salary r C Pearson Correlation Sig. (2-tailed) Sum of Squares and Cross-products Covariance N Pearson Correlation Sig. (2-tailed) Sum of Squares and Cross-products Covariance N Pearson Correlation Sig. (2-tailed) Sum of Squares and Cross-products Covariance N Pearson Correlation Sig. (2-tailed) Sum of Squares and Cross-products Covariance N Correlations *. Correlation is significant at the 0.05 level (2-tailed). **. Correlation is significant at the 0.01 level (2-tailed). Matrix Previous Experience Months Beginning Current Salary (months) since Hire Salary 1 -,097*,084,880**,034,067,000 1,379E , ,5 5,59E , , , ,097* 1,003,045,034,948, , , , , ,281 3, , ,084, ,020,067,948, , , , , ,823 3, , , ,880**,045 -,020 1,000,327, , ,5 2,93E , , , Inverse relationship Direct relationship

9 Assumptions of Pearson s Correlation Coefficient Variables should be measured at the interval or ratio level There needs to be a linear relationship between the two variables There should be no significant outliers Variables should be approximately normally distributed

10 Rank-correlation Spearman rank order correlation coefficient is a nonparametric measure of the strength and of the direction of relation between two variables measured on at least an ordinal scale.

11 Exercise 3 Rank Correlation Ten students were ranked by their mathematical and musical ability: Student Ability A B C D E F G H I J Mathematics Music

12 Analyze / Correlate / Bivariate

13 6 1- n (n d 2 i ρ 2 2 1) (10-1) Strong relationship

14 Linear regression y ŷ = b 0 + b 1 x b 1 : for every 1 unit increase in x we expect y to change by b 1 units b 0 : when x=0, y=b 0 x

15 Exercise 4 Linear Regression File / Open / Employee data.sav Determine a linear relationship between the salary and the age of the employees! Create a new variable!

16 Create a new variable: age = this year date of birth (in year) This year Transform / Compute Variable

17 Analyze / Regression / Linear Regression

18 Model 1 Model Summ ary Adjusted Std. Error of R R Square R Square the Estimate,146 a,021,019 $16, a. Predictors: (Constant), age Multiple correlation coefficient Adjusted multiple determination coefficient R r 2 y1 r 2 y2 2r 1 r y r y2 r It expresses the combined effect of all the variables acting on the dependent variable Weak dependence 12 Multiple determination coefficient How many percent of the variation of the dependent variable can be explained by the variation of all the independent variables The dependent variable (current salary) is explained in 2,1% by the regression model R 2 n 1 1 (1 R n p 1 It enables to compare the multiple determination coefficient among populations / samples with different size and different number of dependent variables as it control for the number of sample / population size (n) and the number of independent variables (p) 2 )

19 F-test: for model testing We can accept the model in every significance level. The F ratio (in the Analysis of Variance Table) is and significant at p=.001. This provides evidence of existence of a linear relationship between the variables

20 Model 1 b 0 b 1 (Constant) age Unstandardized Coefficients Coefficie nts a Standardized Coefficients B Std. Error Beta t Sig , ,686 17,613,000 a. Dependent Variable: Current Salary The regression line: ŷ = b 0 + b 1 x -211,609 66,124 -,146-3,200,001 b 0 : If the x variable is 0, how much is the y. If the employees are 0-year-old, they earn $41543,805 (It doesn t mean anything.) b 1 : If the x increases by 1 unit, what is the difference in y. We can accept the parameters at every significance level. If the employees are 1 year older, they earn less money with $211,609.

21 Exercise 5 - Multiple Regression Determine the characteristics of the current salary in relation with the age, education level, beginning salary, month since hire and previous experience. y = current salary x 1 = age x 2 = education level (years) x 3 = beginning salary x 4 = month since hire x 5 = previous experience

22 Analyze / Regression / Linear y x

23 Output View

24 Output View yˆ ,049x x x x x 5

25 Thanks for your attention