Correlation Chart

Correlation chart shows EMOTSTB and OPTIMISM as the two variables with highest correlation with our dependent variable of CARSAT. OPTIMISIM and ENOTSB both are the highest positively correlated to our target variable CARSAT. Although correlation is super strong.

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTB + CONSCIEN + EXTRAV + TEAMWK + 
##     EXTRAV:TEAMWK, data = ECF_Data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.65964 -0.53820  0.03092  0.60008  2.07982 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.572404   1.105415   0.518    0.605    
## EMOTSTB        0.430008   0.066138   6.502 3.12e-10 ***
## CONSCIEN       0.024884   0.060732   0.410    0.682    
## EXTRAV         0.205155   0.269358   0.762    0.447    
## TEAMWK         0.059856   0.325756   0.184    0.854    
## EXTRAV:TEAMWK -0.003717   0.078537  -0.047    0.962    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8612 on 314 degrees of freedom
## Multiple R-squared:  0.1818, Adjusted R-squared:  0.1687 
## F-statistic: 13.95 on 5 and 314 DF,  p-value: 2.542e-12

This model shows just one independent variable being significant - EMOTSTB The interation between EXTRAV and TEAMWK is not significant.

Model that only contains the significant component

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTB, data = ECF_Data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.64534 -0.54167 -0.01729  0.59247  2.07419 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.45018    0.22410   6.471 3.67e-10 ***
## EMOTSTB      0.48781    0.06293   7.752 1.24e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8676 on 318 degrees of freedom
## Multiple R-squared:  0.1589, Adjusted R-squared:  0.1563 
## F-statistic: 60.09 on 1 and 318 DF,  p-value: 1.236e-13

We see above that there is an adjusted R squared value of 0.16 meaning that 16% of the total variance of CARSAT is made up of this formula that includes just the one independent variable (EMOTSTB). The adjusted R squared value is lower than the R squared value since it takes into consideration the independent variable. The overall model is significant, but not a strong predictor of our dependent variable CARSAT

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

The linear model line above does not fit towards the data super effecivetly with just EMOTSB as an independent variable.

Add the two other variables - OPITIMISM and CUSTERO

## 
## Call:
## lm(formula = CARSAT ~ EMOTSTB + CONSCIEN + EXTRAV + TEAMWK + 
##     OPTIMISM + CUSTSERO + EMOTSTB * OPTIMISM, data = ECF_Data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.73582 -0.52383  0.05134  0.59066  1.96625 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)  
## (Intercept)       0.80711    1.03640   0.779   0.4367  
## EMOTSTB           0.19757    0.30259   0.653   0.5143  
## CONSCIEN          0.02866    0.06133   0.467   0.6406  
## EXTRAV            0.16233    0.07907   2.053   0.0409 *
## TEAMWK            0.05213    0.06600   0.790   0.4302  
## OPTIMISM         -0.03330    0.23977  -0.139   0.8896  
## CUSTSERO          0.05333    0.11379   0.469   0.6396  
## EMOTSTB:OPTIMISM  0.04252    0.07372   0.577   0.5645  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8609 on 312 degrees of freedom
## Multiple R-squared:  0.1876, Adjusted R-squared:  0.1694 
## F-statistic: 10.29 on 7 and 312 DF,  p-value: 1.29e-11

We see that the interaction between EMOTSTB and OPTIMISM is not significant here. In this particular model EXTRAV is the only independent variable coming through as significant.

Let’s now use a model for EXTRAV and EMOTSTB to build a model.

## 
## Call:
## lm(formula = CARSAT ~ EXTRAV + EMOTSTB, data = ECF_Data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.71837 -0.55590  0.03186  0.57402  2.12333 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.78464    0.32115   2.443  0.01510 *  
## EXTRAV       0.20747    0.07246   2.863  0.00447 ** 
## EMOTSTB      0.43295    0.06511   6.649 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.858 on 317 degrees of freedom
## Multiple R-squared:  0.1801, Adjusted R-squared:  0.175 
## F-statistic: 34.82 on 2 and 317 DF,  p-value: 2.133e-14

Here we see the Adj R squared at 0.18 with both independent variables being significant.

Using regression formula for predection

Above is the table showing the predicted values