Type: test statistic.

Measurement level: Correlates: all metric, Happiness: metric.
Range: [-1 ; +1]

Meaning:  
beta > 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta < 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta = 0  «   no correlation.
beta = + 1 or -1  «   perfect correlation.

Type: test statistic.

Measurement level: Correlates: all metric, Happiness: metric.
Range: [-1 ; +1]

Meaning:  
beta > 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta < 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta = 0  «   no correlation.
beta = + 1 or -1  «   perfect correlation.

Type: test statistic.

Measurement level: Correlates: all metric, Happiness: metric.
Range: [-1 ; +1]

Meaning:  
beta > 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta < 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta = 0  «   no correlation.
beta = + 1 or -1  «   perfect correlation.

Type: test statistic.

Measurement level: Correlates: all metric, Happiness: metric.
Range: [-1 ; +1]

Meaning:  
beta > 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta < 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta = 0  «   no correlation.
beta = + 1 or -1  «   perfect correlation.

Type: test statistic.

Measurement level: Correlates: all metric, Happiness: metric.
Range: [-1 ; +1]

Meaning:  
beta > 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta < 0  «  a higher correlate level corresponds to a higher happiness rating on average.
beta = 0  «   no correlation.
beta = + 1 or -1  «   perfect correlation.

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis

Type: test statistic.
Correlate level: metric, Happiness level: metric
Theoretical range: unlimited

The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.
The instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.


See Mardia Kent & Bibby (1979): Multivariate Analysis