## Abstract

Understanding social science studies calls for exploration of various research models that help generate data needed to analyze relations between two entities. The data generated is expected to present two variables that are compared empirically to make it easy to associate the variables in their different entities and how they influence each other. This paper seeks to explore the regression model of research. The three models of regression are the focal point for the observation done and they include linear, logistical, and spline regression. The type of data collected by the regression model is explored and described in detail. Additionally, the findings and analysis of the possible data to be collected is done to predict possible outcomes should the model be adopted for research.

** **Introduction and Method

The regression model allows observations to be made on variables that influence the results of the research. The possible observation that could be made from the regression model is either positive or negative. The negative observation is against the hypothesis of the research while positive observation supports the hypothesis. The regression model broken into the three models generates different data that is used to analyze the thesis of the research. Considering linear regression, the technique is applied to produce a connection between dependent and independent variables. Linear regression can be used to predict possible conclusions for dependent variables in instances where independent variables are distorted. Usually, the model employs the linear equation Y=b0+∑ (bi Xi) +e to explain the different variables of the observation. From the equation Y is the dependent variable while Xi represents independent variables. The other symbols stand for constant in the equation.

Another regression model is logistical regression which is the probability of the outcomes of the research are ascertained. The model is based on binary outcomes represented by 0 and 1. Logistical regression is also represented in an equation that simplifies the findings. The equation expresses the probability symbolizes by Y as the dependent variables in which case Y= P (Y=1) =1/1+e− (b0+∑ (bi Xi)). The independent variable in this case is Xi which could be binary or continuous. The rest of the symbols are representatives of coefficients of values that change in odds of Y as Xi changes. The binary presentation of logistical regression data 0 and 1 represent negative and positive observations where 0 is negative and 1 is positive. Spline regression on the other hand is the prediction of values of dependent variables from a collection of independent variables. The findings are expressed in an equation Y_{i} = mu (x_{i}) in which Y is the dependent variable, i is the sequence of observations made mu is the differentiable function and X is the independent variable.

#### Data

The data that would be generated from the model is quantitative data given that the regression model entails experiment based data. Qualitative data is essential to the model since it is quantifiable. The quantified data is easily understood and can be manipulated statistically to generate a series of numerical values that define the essence of the research as far as the hypothesis is concerned. Qualitative data is described as ordinal because it is logical and follows an order. The independent variables in the data are not influenced by the changes that occur during the observation process in the research. Independent variables differ from one research to another. Examples of possible independent variables are age, height and size. Dependent variables are influenced by independent variables and they change depending on the changes in the independent variables. Independent and dependent variables can be operationalized through statistical manipulations to become quantifiable. Additionally, the data can be collected through questionnaires where the researcher selects a group of subjects and hands questionnaires to be filled. The data collected is then classified as independent or dependent variables to enable statistical manipulation on the data. The questionnaires should be closed since quantitative data requires specific information.

Another means of gathering the data would be through interviews where the researcher interviews the selected subject matter to gather the relevant information on the research. The interviews done would be cognitive to generate yes or no answers which are useful for quantitative data. Such data is precise and direct which produces ordinal data that is critical for quantitative data collected. Surveys are also used to generate information for the research. The surveys may be conducted over a period of time to produce several data for comparison and verification. It is imperative that the research uses the same subjects to ensure that the results are logical. Polls are also used where the subject matters is subjected to a poll in which they chose between two variables to establish the preferences they have towards independent data. Although using computational techniques to manipulate pre-existing data is minimally used, it can be employed in the regression model to develop a set of data for the research. Such data is not popular with the model because it is borrowed from prior studies and could be disqualified as real data.

#### Findings and Results

From the empirical tests, it can be concluded that regression is essential to test social sciences. The model could be broken down into three models that are used to prove the hypothesis of the research. The independent variables represented by X in all the three models of regression are influenced by change in Y which is dependent variables. The models apply the same technique with different data considerations to produce information that develops the conclusion of the research by affirming the hypothesis of the research. From the regression, i is the sequence of observations of the data observed, mu is the differentiable function, the constant e, and b. Y is equaled to X with mathematical manipulations of other coefficients such as the sequence of observation, differentiable function and constants.

Y in the regression equation represents the positive results of the hypothesis for linear and spline regression and X represents the negative results of the hypothesis. In logistical regression the data is represented in binary form of 0 and 1 thereby, the 0s of the data are negative and the 1s are positive results of the hypothesis in the research. The method used in collecting data is complimentary to the regression models of research. Qualitative method would be ideal considering it is empirical based thus, it generates the needed information for the statistical manipulation to complete the research. Some of the methods of qualitative research are generate specific data that are essential for regression model of research. They produce numerical data or data that is easily transformed into numbers that are used in the regression equations to develop the evidence required to prove the hypothesis. The model could be proven improper if the Y and X values are similar. This would be against the principle of regression model where there are two variables that are inversely proportional to eh other. The data collected could also be used for the t-test model of research. The regression model of research demands alertness in recording information to avoid ambiguity in the data collected that could render the model improper for the subject matter of research.