Quantifying Connections: Unraveling Bivariate Relationships with Pearson Correlation Coefficient

Findings

Bivariate Pearson correlation coefficient test and partial correlation test (Appendix 1 and 2) :

Pearson correlation coefficient is a technique for investigating the relationship between two quantitative, continuous variables. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables. The correlation analysis provides partial confirmation of the core. When Pearson’s correlation value is greater than 0.5 and close to 1, it depicts a strong positive correlation between two variable. When Pearson’s correlation value is less than 0.5 but greater than zero, it depicts a week positive correlation between two variable. Significant value (2 tailed) is .000 which is lower than .05, depicts that there is a statistically significant correlations between two variables and significant value (2 tailed) is .000 which is greater than .05, depicts that there is no statistically significant correlations between two variables. A scatterplot is a valuable summary of an established of bivariate data (Wright, 2014). Scatterplot is done between for understanding the relation or association of two variables at a glance. For those seeking additional insights or assistance, statistics dissertation help can provide the necessary support to enhance your analysis.

Housing: There are four measures are indicated for housing.

Housing cost measure:

According to the result, it was found a strong, positive and significant correlation between wellbeing score and median housing cost as the correlation coefficient value is reported as .541 which is greater than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the value of partial correlation of variable wellbeing score with median housing cost while controlling the effect of median household income was reported as .280 depicted a significant good association. While controlling household income small variation had occurred. The following scatter plot of these two variables demonstrate the appearance of associated variables as partial linear pattern is recognized.

Housing Affordability:

According to the result, a strong, positive and significant correlation between wellbeing score and Housing Affordability as the correlation coefficient value is reported (.566) which is greater than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as .340 and significant value is .000 which also depicted strong relation. The following scatter plot of these two variables demonstrate the appearance of associated variables as linear pattern is recognized.

Homeownership rate

According to the result, a weak positive and significant correlation between wellbeing score and Homeownership rate as the correlation coefficient value is reported (.067) which is less than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as -.064 and significant value is .000 which also depicted a negative association. The following scatter plot of these two variables demonstrate the appearance of partially associated variables as no particular pattern is recognized.

Housing Size

According to the result, a moderate positive and significant correlation between wellbeing score and Housing Size as the correlation coefficient value is reported (.287) which is less than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as .197 and significant value is .000 which also depicted a moderate positive association. The following scatter plot of these two variables demonstrate the appearance of partially associated variables as no particular pattern is recognized.

Income:

Median Household Income:

According to the result, a strong, positive and significant correlation between wellbeing score and Median Household Income as the correlation coefficient value is reported (.507) which is greater than 0.5 and significant value (2 tailed) is .000 which is lower than .05. The following scatter plot of these two variables demonstrate the appearance of associated variables as linear pattern is recognized.

Average wages

According to the result, a moderate positive and significant correlation between wellbeing score and Housing Size as the correlation coefficient value is reported (.265) which is less than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as .022 and significant value is .000 which also depicted weak positive relation. The following scatter plot of these two variables demonstrate the appearance of partially associated variables as no particular pattern is recognized.

Unemployment Rate

According to the result, negative and significant correlation between wellbeing score and unemployment rate as the correlation coefficient value is reported (- 0.334) which is less than 0 and significant value (2 tailed) is .000 which is lower than 0. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as -0.085 and significant value is .000 which also depicted a significant negative relation. The following scatter plot of these two variables demonstrate the appearance of non-associated variables as no pattern is recognized.

Education

According to the result, a moderate positive and significant correlation between wellbeing score and Housing Size as the correlation coefficient value is reported (.360) which is less than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as .111 and significant value is .000 which also depicted a moderate positive relation. The following scatter plot of these two variables demonstrate the appearance of partially associated variables as no particular pattern is recognized.

Population Density

According to the result, a weak positive and significant correlation between wellbeing score and Population Density as the correlation coefficient value is reported (.168) which is less than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as .020 and significant value is .000 which also depicted a moderate positive relation. The following scatter plot of these two variables demonstrate the appearance of partially associated variables as no particular pattern is recognized.

Age

According to the result, a weak positive and significant correlation between wellbeing score and age as the correlation coefficient value is reported (.067) which is less than 0.5 and significant value (2 tailed) is .000 which is lower than .05. According to the result of partial correlation of those variable while controlling the effect of median household income was reported as -.013 and significant value is .000 which also depicted a negative relation. The following scatter plot of these two variables demonstrate the appearance of partially associated variables as no particular pattern is recognized.

Model 1 (Appendix 3)

The first model was run with all the independent variables. According to the model fitting information, the significant value came out less than 0.005 which proves that the model was valid. According to the coefficient table, the significance value of some variables comes more than 0.05, that’s why this variables was removed from the model and final model is selected with only those independent variables whose signifance value is lesser than 0.05. Those variables which are selected for making the predictive model of wellbeing score are annual mean wage, age, median housing value, housing affordability, housing size and home ownership rate as significance (p) value is less than .05 which proved that independent variables statistically significantly predict the dependent variable.

Model 2(Appendix 4)

The second model has been established with 6 independent variables which variables are describing significantly the model. Multicollinearity detection test also have been done through the Variance Inflation Factor, which is just the reciprocal of the tolerance statistics. A VIF of greater than or equal to 10 is generally considered as evidence of multicollinearity. This model has some multicollinearity issue. A value of R, 0.64, indicates such a decent level of forecasting wellbeing score by this selected model. This model is able to explain 41% of the dependent variable which is not bad and each and every independent variable is giving significantly to the model according to the result of model 2 summary.

Model 3 (Appendix 5)

As the main aim of the study is to evaluate the impact of the housing variables on well-being score , that’s why next model was designed with only housing variables like median housing value, housing affordability, housing size and home ownership rate. According to the model fitting information, the significant value came out less than 0.005 which proves that the model was valid. According to the coefficient table, the significance value of median housing value comes more than 0.05, that’s why this variables was removed from the model and high VIF ,which is investigated for multicollinearity , was noted in median housing value and housing affordability. This model has some multicollinearity issue. A value of R, 0.59, indicates such a decent level of forecasting wellbeing score by this selected model. This model is able to explain 34% of the dependent variable. The significance values median housing value is noted more than 0.05 that’s why the variable is removed and final model is selected.

Model 4 (Appendix 6)

According to the model fitting information, the significant value came out less than 0.005 which proves that the model was valid. According to the co efficient table all VIF are lied in 1-1.4 which depicts that there is no multicollinearity in the model. Significance value of all independent variable comes out less than 0.05 and a value of R, 0.59, indicates such a decent level of forecasting wellbeing score by this selected model. This model is able to explain 34% of the dependent variable and it means only 3 variables of housing, can together explain 59% of the dependent variable wellbeing score.