Multiple Regression Model Formulation

Answer

Multiple Regression Model Formulation

Multiple linear regression is an improved form of the simple or bivariate linear regression. In this case, the influence of more than one independent variable on a single dependent variable is examined. Therefore, multiple linear regression analysis is associated with exploration of a single dependent or response variable and multiple/several independent or explanatory variables (Frankfort-Nachmias, & Leon-Guerrero, 2017). In multiple regression model, two or more independent variables are used to predict the dependent variable. The general purpose of multiple regression, that also influenced its formulation in the early 20^th century, is enhanced expositive examination of the relationship between several independent variables and a dependent variable, the model therefore is a linear expression of this relationship (Wagner, 2016). In the process of multiple regression modeling, certain assumptions like linearity, homoscedasticity, non-multicollinearity and normality have to be made. This paper reports on a multiple regression analysis model formation based on the General Social Survey dataset.

Model Formation

The research question for the study is: does an individual’s weekly hours of work and the degree of education have a significant effect on their income? The research question seeks to establish a correlation between the level of income and the level of an individual’s education and the duration of weekly work reporting. The null hypotheses for the research questions is:

• The degree of education and an individual’s hours of work have no significant effect on income.

Being an experimental study with greater internal validity the research design that would align with the question is randomization design. The experiment will be repeated under uniform investigational conditions as the participants will be assigned different treatment and control groups. The approach will establish an evidence of causation between the variables of income, work hours, weekly reporting or hours spent watching television, by showing the existing associations between them. The approach has the capacity to sort out the magnitude and existence of causal effects of one or more independent variables upon a dependent variable of interest at a given time. Randomization will facilitate assigning of participants to various groups to eliminate selection bias and any confounding bias while ensuring the associate groups are comparable regardless of any other factors other than the ones under investigation.

The dependent variable was individual’s income (measured by scales of respondents’ income). It was the researcher’s major point of interest in determining possible changes to the dependable variable. The research establishes change in income as influenced by working duration recorded working hours per week), and the level of education measured by degree attained by the respondent). The variable was measured by establishing a causal relationship between the four metric variables, one continuous dependent variable and three more independent variables. The assumption behind the multiple regression analysis was that the independent variables have a direct effect on the stability of income as the dependent variable.

Results

Table 1: Model summary table.

The model formulated explains 57.6% variance of the response variable. The ANOVA test confirms the significance of the model, with p-value < 0.05.

Table 2: regression table of the formulated model.

The t-test indicates that the IVs are significant explanatories in the model. The p-values < 0.05 leads us to reject the null hypothesis of no relationship, and further, the correlation coefficients confirm the degree of linear relationship between the independent variables and the dependent variables. Therefore, there is a significant linear correlation between Income and the two independent variables (level of education and the time duration employed in delivering work). These two variables, therefore, effect the level of income independently.

The model therefore, is

Y = 1.492 + 0.687X₁ + 0.17X₂ + 2.318

Where Y denotes the Income Variable.

X₁ denotes the Education level variable

X₂ denotes the number of hours worked in a week.

Further, the IVs are controlled and changed in a scientific experiment to determine the extent of their effects on the dependent variable. The nature of employment variable (whether self-employed or works for somebody) is used to control the effects of these variables. This is determined by the hypothetical thought that this variable is likely to consistently affect income. The results are as follows:

Table 3: Regression table with control variable.

While the control is not a significant predictor (p-value > 0.05), its effect on the model is significant as its inclusion in the model increases the r-squared value (with inclusion of nature of employment, 61% variation in the response variable is explained, which is way more than the 57.6% explained without it). The control variable also alters the effect of the controlled IVs as in table 3 above. However, the order of importance of the variables ranks it as the least among predictors.

Therefore, Number of hours of work and level of education significantly influences an individual’s income. From the model, it is clear that the higher the education level attained, the more likely is it for one to get higher income, and higher number of working hours impacts higher income. That is the linear relationship between the two variables. The two variables combined explains 56.7% of the income possibilities. However, with an inclusion of the nature of employment of an individual (whether self-employed or employed by someone), the income possibilities are explained at 61% in prediction. The model above can be used to predict an individual’s income with the percentage variation possibilities explained.