Data and Empirical Approach: Using a Data Set To Test Any Relationships Between Academic Success and 5 Variables

Introduction:

This study’s goal is to investigate the connection between academic success and several variables that may be associated with it. Academic success is a broad construct encompassing various academic outcomes, including grades, test scores, and graduation rates. This study will analyze the effects of five independent factors on grades as the dependent variable: parental education level, hours spent studying per week, class attendance, self-efficacy, and ethnicity. The five independent variables chosen for this study are important factors that may influence a student’s grade. Parental education level is important because it can influence the level of expected academic performance from the student and how much support the student receives from their family. Hours spent studying per week can also significantly impact grades as it reflects how much effort the student is putting into their studies. Class attendance is also important as it can directly affect a student’s ability to successfully understand and retain material taught in class. Self-efficacy is also important as it reflects the student’s belief in their ability to complete tasks. Lastly, ethnicity is important to consider as it can influence the support a student receives from their peer group. These variables are important to consider when examining the influence of grades. We will employ a quantitative research design to analyze data collected from a survey of college students. The data will be analyzed using descriptive and inferential statistics, including correlation and regression analyses, to examine the strength and characteristics of the connection between the independent variables and academic success. The results of this study will provide valuable insight into the factors that influence academic success, which can help educators and policymakers better understand and address the needs of college students.

Data:

The data for this study come from a survey conducted at a huge scale, a public United States University. The survey was administered to undergraduate students in their third year of study. The survey included questions about various aspects of the student’s academic experiences and demographic information.

In this table, Grades are the dependent variable, while Parental Education Level, Study Hours, Class Attendance, Self-Efficacy, and Ethnicity are the independent variables.

We chose to include Parental Education Level as an independent variable because prior research has suggested that parental education is positively related to academic success (Gutman & Midgley, 223-249). We chose to include Study Hours and Class Attendance because prior research has suggested that these factors positively affect the academic success (Credé et al., 272-295). We chose to include Self-Efficacy because prior research has suggested that it is positively related to academic success (Bandura, 75-78). Finally, we chose to include Ethnicity as an independent variable because prior research has suggested that ethnic minority students may face unique challenges in academic settings that could affect their academic success (Umaña-Taylor et al., 2034-2050).

Empirical Approach:

To examine the relationship between Grades and the five independent variables, we plan to use multiple linear regression analysis. This approach allows us to estimate the independent effects of each variable on Grades, adjusting for the impact of the other factors in the model. Specifically, we will estimate the following regression equation:

Grades = β0 + β1(Parental Education Level) + β2(Study Hours) + β3(Class Attendance) + β4(Self-Efficacy) + β5(Ethnicity) + ε

In this equation, β0 represents the intercept, β1-β5 represent the regression coefficients

Potential Problem

One potential problem with the above estimation technique is heteroskedasticity (Anselin 141-163). It occurs when the variance in the residuals is not constant across the range of the independent variables. This might result in inaccurate regression coefficient estimates and misleading inferences regarding the connections between the dependent and independent variables. To address this problem, it is important to use transformations of the independent variables and to test for heteroskedasticity using statistical tests such as the Breusch-Pagan and White tests. Additionally, using weighted least squares or robust regression methods that are more robust to heteroskedasticity may be beneficial.

The most common way to address heteroskedasticity is by transforming the independent variable. This can be done by taking the independent variable’s natural logarithm (log) or by squaring or cubing it. This transformation can help to reduce the degree of heteroskedasticity and make the regression model more robust. Additionally, it is important to check the residuals of the regression model for signs of heteroskedasticity. This can be done by running a Breusch-Pagan test or a White test. If either test suggests the presence of heteroskedasticity, then it is important to take steps to address it. Finally, it may also be beneficial to use weighted least squares or robust regression methods that are more robust to heteroskedasticity.

Another potential problem is endogeneity (Larcker et al., 207-215). It occurs when the independent variables are correlated with the error terms. This may result in skewed estimations of the regression coefficients and provide false findings about the relationships between the independent and dependent variables. To address this issue, researchers can use instrumental variables or use a two-stage least squares regression.

Overall, the main problems associated with OLS regression are multicollinearity, heteroscedasticity, autocorrelation, and endogeneity. To address these issues, researchers should use techniques such as regularization, robust standard errors, and instrumental variables. Endogeneity occurs when the independent variables in a regression correlate with the equation’s error term. To address endogeneity, one could use instrumental variables (IV) estimation. In IV estimation, one uses an instrument, an exogenous variable correlated with the endogenous variable, to estimate the equation. The instrumental variable is assumed to have no direct effect on the dependent variable, but it is correlated with the endogenous variable and influences it. Using this as an instrument, one can estimate the equation and obtain unbiased estimates of the coefficients.

A third potential problem is non-stationarity (Stewart et al., 605-627). Non-stationarity occurs when the mean of the residuals is not constant across the range of the independent variables. This can lead to biased regression coefficient estimates and incorrect conclusions about the relationships between the independent and dependent variables. The non-stationarity can be identified using the residual plot or statistical tests. To fix this issue, the data should be transformed using techniques such as detrending, differencing, or transformations such as logarithmic, exponential, or polynomial to make the data more stationary.

Overall, linear regression is a powerful tool for analyzing the relationships between independent and dependent variables but can be susceptible to potential problems such as multicollinearity, heteroscedasticity, and non-stationarity. To ensure that the model is reliable and valid, it is important to be aware of these potential issues and take steps to address them. To address the non-stationarity problem, an approach known as the Difference Method can be used. This method involves taking the difference between the current and previous values to create a stationary time series. This approach can identify relationships within the time series that may not have been visible. For example, it can detect linear and nonlinear trends and make predictions about future values. Additionally, it can also be used to identify seasonality and other cycles in the data.

A fourth potential problem is a multicollinearity (Mason et al., 268-280). Multicollinearity occurs when the independent variables are highly correlated with each other. This can lead to biased regression coefficient estimates and incorrect conclusions about the relationships between the independent and dependent variables. This can be addressed by looking at the correlation matrix and removing highly correlated variables. Additionally, regularization techniques, such as ridge regression, can also be used to reduce the effects of multicollinearity.

Overall, these four potential problems potentially result in skewed estimations of the regression coefficients and false findings about the relationships between independent and dependent variables. Therefore, it is important for researchers to be aware of these potential problems and take steps to address them if necessary. One technique that can be used to diagnose a multicollinearity problem is Factor for Variance Inflation (VIF). VIF is a measure of the extent to which a predictor variable is linearly related to other predictor variables in a regression model. A VIF value greater than 5 indicates a potential multicollinearity problem. In this case, it is recommended to remove any predictor variables that have high VIF values, as these predictor variables are likely to be redundant.

Discussion

Based on the data provided, we plan to use multiple linear regression analysis to examine the relationship between Grades and the five independent variables: Parental Education Level, Study Hours, Class Attendance, Self-Efficacy, and Ethnicity. Multiple linear regression analysis is an appropriate choice for examining the relationship between Grades and the five independent variables because it is a statistical tool that allows us to analyze multiple independent variables at once and determine how they are related to the dependent variable. The effect of each independent variable on the dependent variable, in this case Grades, may be measured using this method. Analysis can also help us identify which variables have the most influence on Grades, so that we can target our interventions and resources accordingly. The regression equation we will estimate is:

Grades = β0 + β1(Parental Education Level) + β2(Study Hours) + β3(Class Attendance) + β4(Self-Efficacy) + β5(Ethnicity) + ε

When all other independent variables in the model are at zero, the intercept 0 indicates the anticipated value of Grades. The coefficients 1 through 5 show how Grades should change if each independent variable is increased by one unit while keeping the other independent variables fixed.

Parental Education Level: This variable represents the highest level of education attained by the student’s parents. The mean score for this variable is 2.40, which indicates that, on average, the parents of the students have completed some college education. The minimum value is 1.0, indicating that some parents have completed only high school, while the maximum value is 5.0, indicating that some parents have completed graduate or professional education.

Study Hours: This variable represents the number of hours the student spends studying per week. The mean score for this variable is 12.5, revealing that students spend 12.5 hours a week studying on average. The minimum value is 5.0, indicating that some students spend very little time studying, while the maximum value is 30.0, indicating that some students spend a lot of time studying.

Class Attendance: This variable represents the percentage of classes the student attends. The mean score for this variable is 85.0%, indicating that, on average, students attend about 85% of their classes. The minimum value is 40.0%, indicating that some students attend very few classes, while the maximum value is 100.0%, indicating that some students attend all their classes.

Self-Efficacy: This variable represents the degree to which the student believes they can achieve academic success. The mean score for this variable is 4.20, indicating that, on average, students have a high level of self-efficacy. The minimum value is 1.0, indicating that some students have very low self-efficacy, while the maximum value is 5.0, indicating that some students have very high self-efficacy.

Ethnicity: This variable represents the student’s self-reported ethnicity. The mean, minimum, and maximum values are not provided in the data, indicating that there is no numerical score associated with this variable.

The ethnicity variable is not reported, so we cannot make any specific observations about it. However, it is included in the regression equation as a control variable, which allows us to account for any potential confounding effects of ethnicity on the relationship between the other independent variables and Grades.

Overall, multiple linear regression analysis will provide a useful tool to investigate the relationships between Grades and independent variables, and to quantify the independent effects of each variable while adjusting for the impact of the model’s other variables.

Work Cited

Anselin, Luc. “Some robust approaches to testing and estimation in spatial econometrics.” Regional Science and Urban Economics 20.2 (1990): 141-163.

Bandura, Albert. “Exercise of human agency through collective efficacy.” Current directions in psychological science 9.3 (2000): 75-78.

Credé, Marcus, Sylvia G. Roch, and Urszula M. Kieszczynka. “Class attendance in college: A meta-analytic review of the relationship of class attendance with grades and student characteristics.” Review of Educational Research 80.2 (2010): 272-295.

Gutman, Leslie Morrison, and Carol Midgley. “The role of protective factors in supporting the academic achievement of poor African American students during the middle school transition.” Journal of youth and adolescence 29.2 (2000): 223-249.

Larcker, David F., and Tjomme O. Rusticus. “Endogeneity and empirical accounting research.” European Accounting Review 16.1 (2007): 207-215.

Mason, Charlotte H., and William D. Perreault Jr. “Collinearity, power, and interpretation of multiple regression analysis.” Journal of marketing research 28.3 (1991): 268-280.

Stewart Fotheringham, A., Martin Charlton, and Chris Brunsdon. “The geography of parameter space: an investigation of spatial non-stationarity.” International Journal of Geographical Information Systems 10.5 (1996): 605-627.

Umaña‐Taylor, Adriana J., et al. “Trajectories of ethnic–racial identity and autonomy among Mexican‐origin adolescent mothers in the United States.” Child development 86.6 (2015): 2034-2050.