Correlation Chart

Correlation chart shows EMOTSTAB and CUSTERO as the two varaibles with highest correlation with our dependent variable of CARSAT. OPTIMISIM and EMOTSTAB both are decently postively correlated at over 0.6 which is the strongest correlation compared to any of the other variables.

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTAB + CONSCIEN + EXTROVER + TEAMWORK + 
##     TEAMWORK * EXTROVER, data = ECF_Data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5551 -0.4942  0.1879  0.6951  1.9205 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        1.37690    1.39438   0.987    0.324    
## EMOTSTAB           0.54180    0.09393   5.768  2.2e-08 ***
## CONSCIEN           0.10208    0.08956   1.140    0.255    
## EXTROVER           0.01949    0.36472   0.053    0.957    
## TEAMWORK          -0.22583    0.38711  -0.583    0.560    
## EXTROVER:TEAMWORK  0.06868    0.09964   0.689    0.491    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.026 on 268 degrees of freedom
## Multiple R-squared:  0.206,  Adjusted R-squared:  0.1912 
## F-statistic: 13.91 on 5 and 268 DF,  p-value: 4.338e-12

This model shows just one independent variable being significant - EMOSTAB

Model that only contains the significant component

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTAB, data = ECF_Data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3984 -0.4845  0.2571  0.7108  2.1312 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.55776    0.32527   4.789 2.76e-06 ***
## EMOTSTAB     0.65553    0.08723   7.515 8.23e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.04 on 272 degrees of freedom
## Multiple R-squared:  0.1719, Adjusted R-squared:  0.1689 
## F-statistic: 56.48 on 1 and 272 DF,  p-value: 8.232e-13

We see above that there is a R squared value of 0.17 meaning that 17% of the total variance of CARSAT is made up of this formula that includes just the one independent variable (EMOTSTAB). The adjusted R squared value is lower since it takes into consideration the independent variable. The overall model is significant, but not a strong predictor of our dependent variable EMOTSTAB.

## `geom_smooth()` using formula 'y ~ x'

Add the two other variables - OPITIMISM and CUSTERO

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTAB + CONSCIEN + EXTROVER + TEAMWORK + 
##     OPTIMISM + CUSTSERO + EMOTSTAB * OPTIMISM, data = ECF_Data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3463 -0.5291  0.1707  0.6703  1.7049 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        0.71869    1.49474   0.481    0.631    
## EMOTSTAB           0.04314    0.41619   0.104    0.918    
## CONSCIEN           0.05418    0.08534   0.635    0.526    
## EXTROVER           0.06980    0.10736   0.650    0.516    
## TEAMWORK           0.01593    0.09787   0.163    0.871    
## OPTIMISM          -0.49938    0.37208  -1.342    0.181    
## CUSTSERO           0.66294    0.11907   5.568 6.31e-08 ***
## EMOTSTAB:OPTIMISM  0.11929    0.10530   1.133    0.258    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9689 on 266 degrees of freedom
## Multiple R-squared:  0.2976, Adjusted R-squared:  0.2791 
## F-statistic:  16.1 on 7 and 266 DF,  p-value: < 2.2e-16

We see that the interaction between EMOTSTAB and OPTIMISM is significant here. However, in this model EMOTSTAB is not. The R squared value is at nearly 0.30. But, lets only use the significant independent variable.

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTAB * OPTIMISM, data = ECF_Data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4296 -0.4783  0.2303  0.6789  1.9354 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)   
## (Intercept)         4.6008     1.4434   3.187   0.0016 **
## EMOTSTAB           -0.3628     0.4324  -0.839   0.4022   
## OPTIMISM           -0.7646     0.3929  -1.946   0.0527 . 
## EMOTSTAB:OPTIMISM   0.2511     0.1095   2.293   0.0226 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.033 on 270 degrees of freedom
## Multiple R-squared:  0.1899, Adjusted R-squared:  0.1809 
## F-statistic: 21.09 on 3 and 270 DF,  p-value: 2.631e-12

Here we see the Adj R squared at 0.18 with the interaction.

Using regression formula for predection

Above is the table showing the predicted values