Sample:
Regression Analysis
Uzorak dijela rada: Regression Analysis
Red text > of the note.
4 Regression Analysis
REGRESSION
see file Regresion_2kF0515.xlsx
High correlations among predictors indicate it is likely that there will be a problem with multicollinearity.
1 The p value is statistically significance at <0.05 <0.01 <0.001
2 Beta is statistically significance in a range from 1 to +1.
3 R2 is statistically significance when his value ir range between 0% and 100%
Model Summary^{b} 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
Change Statistics 

R Square Change 
F Change 
df1 
df2 
Sig. F Change 

1 
,571^{a} 
,326 
,292 
1,045 
,326 
9,522 
6 
118 
,000 
a. Predictors: (Constant), COUNTRY OF IMAGE, MATERIALISM, SUSCEPTIBILITY TO NORMATIVE INFLUENCE, NEED FOR UNIQUENESS, BRAND CONSCIUSNESS, SOCIAL COMPARISON 

b. Dependent Variable: PURCHASE INTENTION 
Multiple correlation coefficient R=0,571 .
Indicates that 29,2% of the variance can be predicted from the independent variables.
The Model Summary table shows that the multiple correlation coefficient (R), using all the predictors simultaneously, is 0,571 (R^{2}=0,326) and the adjusted R^{2}is 0,292, meaning that 29,2% of the variance can be predicted from the independent variables. Note that the adjusted R^{2} is lower than the unadjusted R^{2}. This is, in part, related to the number of variables in the equation. The adjustment is also affected by the magnitude of the effect and the sample size. As you will see from the coefficients table, only MATERIALISM, NEED FOR UNIQUENESS and COUNTRY OF IMAGEare significant, but the other variables (BRAND CONSCIUSNESS, SOCIAL COMPARISON and SUSCEPTIBILITY TO NORMATIVE INFLUENCE ) will always add a little to the prediction. Because so many independent variables were used, a reduction in the number of variables might help us find an equation that explains more of the variance in the dependent variable. It is helpful to use the concept of parsimony with multiple regression, and use the smallest number of predictors needed.
ANOVA^{a} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
62,435 
6 
10,406 
9,522 
,000^{b} 
Residual 
128,957 
118 
1,093 



Total 
191,392 
124 




a. Dependent Variable: PURCHASE INTENTION 

b. Predictors: (Constant), COUNTRY OF IMAGE, MATERIALISM, SUSCEPTIBILITY TO NORMATIVE INFLUENCE, NEED FOR UNIQUENESS, BRAND CONSCIUSNESS, SOCIAL COMPARISON 
Indicates that the combination of these variables significantly (p <0 ,001) predicts the dependent variable.
The ANOVA table shows that F= 9,522 and is significant. This indicates that the combination of the predictors significantly predict PURCHASE INTENTION.
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 
95,0% Confidence Interval for B 
Correlations 
Collinearity Statistics 

B 
Std. Error 
Beta 
Lower Bound 
Upper Bound 
Zeroorder 
Partial 
Part 
Tolerance 
VIF 

1 
(Constant) 
,311 
,618 

,502 
,616 
,914 
1,535 





BRAND CONSCIUSNESS 
,114 
,134 
,083 
,853 
,396 
,151 
,380 
,378 
,078 
,064 
,603 
1,659 

MATERIALISM 
,278 
,108 
,234 
2,569 
,011 
,064 
,492 
,413 
,230 
,194 
,686 
1,457 

SOCIAL COMPARISON 
,052 
,100 
,052 
,518 
,605 
,146 
,250 
,319 
,048 
,039 
,559 
1,790 

SUSCEPTIBILITY TO NORMATIVE INFLUENCE 
,058 
,111 
,053 
,524 
,601 
,277 
,161 
,267 
,048 
,040 
,560 
1,785 

NEED FOR UNIQUENESS 
,279 
,110 
,231 
2,540 
,012 
,062 
,497 
,449 
,228 
,192 
,688 
1,453 

COUNTRY OF IMAGE 
,244 
,112 
,210 
2,172 
,032 
,021 
,466 
,437 
,196 
,164 
,610 
1,639 

a. Dependent Variable: PURCHASE INTENTION 
Only MATERIALISM, NEED FOR UNIQUENESSand COUNTRY OF IMAGEare significantly contributing to the equation. However, all of the variables need to be included to obtain this result, since the overall F value was computed with all the variables in the equation.
The table of correlation can be seen that there is a positive (or negative) impact. And can see how strong the connection/impact.
From Chisquare to see whether a statistically significant relationship.
From reations see the formula for the calculation.
PURCHASE INTENTION=0,31 + (0,114 x BRAND CONSCIUSNESS) + (0,278 x MATERIALISM) + (0,052 x SOCIAL COMPARISON) + (0,058 x SUSCEPTIBILITY TO NORMATIVE INFLUENCE) + (0,279 x NEED FOR UNIQUENESS) + (0,244 x COUNTRY OF IMAGE) (from column B )
The table of correlation can be seen that there is a positive (or negative) impact. And can see how strong the connection/impact.
From Chisquare to see whether a statistically significant relationship.
From reations see the formula for the calculation.
Tolerance and VIF give the same information. (Tolerance = 1 /VIF) They tell us if there is multicollinearity. If the Tolerance value is low (< 1R^{2}), then there is maybe probably (do not necessarily a problem, because it is little difference ) a problem with multicollinearity. In this case, since adjusted R^{2} is 0.326, and 1 R^{2} is about 0.674, then tolerances are low for BRAND CONSCIUSNESS, SOCIAL COMPARISON and COUNTRY OF IMAGE.
One of the most important tables is the Coefficients table. It indicates the standardized beta coefficients.
The t value and the Sig opposite each independent variable indicates whether that variable is significantly contributing to the equation for predicting PURCHASE INTENTION from the whole set of predictors. Thus, MATERIALISM, NEED FOR UNIQUENESSand COUNTRY OF IMAGE, in this example, are the only variables that are significantly adding anything to the prediction when the other variables (BRAND CONSCIUSNESS, SOCIAL COMPARISON and SUSCEPTIBILITY TO NORMATIVE INFLUENCE ) are already considered. It is important to note that all the variables are being considered together when these values are computed. Therefore, if you delete one of the predictors that is not significant, it can affect the levels of significance for other predictors.
Collinearity Diagnostics^{a} 

Model 
Eigenvalue 
Condition Index 
Variance Proportions 

(Constant) 
BRAND CONSCIUSNESS 
MATERIALISM 
SOCIAL COMPARISON 
SUSCEPTIBILITY TO NORMATIVE INFLUENCE 
NEED FOR UNIQUENESS 
COUNTRY OF IMAGE 

1 
1 
6,828 
1,000 
,00 
,00 
,00 
,00 
,00 
,00 
,00 
2 
,056 
11,027 
,04 
,01 
,00 
,36 
,14 
,08 
,02 

3 
,032 
14,517 
,02 
,04 
,33 
,08 
,02 
,12 
,25 

4 
,028 
15,530 
,00 
,02 
,14 
,44 
,69 
,00 
,00 

5 
,020 
18,264 
,01 
,22 
,02 
,00 
,09 
,67 
,31 

6 
,018 
19,547 
,73 
,44 
,02 
,00 
,02 
,09 
,00 

7 
,017 
20,039 
,19 
,28 
,49 
,13 
,04 
,03 
,41 

a. Dependent Variable: PURCHASE INTENTION 
This tells you how much each variable is contributing to any collinearity in the model.