RESEARCH METHODS

Introduction

Simple linear regression is expanded upon by multiple regression when predicting the value of a variable against the values of two or more other variables (Uyanik, & Guler, 2013). The dependent variable is the one that has to be predicted, whilst the independent variables are used to predict the value of the dependent variable (Arayesh, 2015). One of the benefits of using multiple regression is to assess the model’s overall fitness (variance explained), and the relative contributions of each predictor to the overall variance explained (Kang, Zhao, 2020). Given this, the three primary tables were interpreted using the multiple regression procedure.

Interpretation of tables

This section of the questions presents the interpretation of three primary tables analysed using the multiple regression procedure.

Table 1: Model Summary

The R column of the multiple regression coefficients measures the quality of the prediction of the dependent variables (science score). Therefore, a value of 0.699 indicates a good level of prediction. Again, the R Square measures the proportion of the dependent variable’s variance that the independent variable can account for. In the table, the value of 0.489 implies that independent variables (reading score, social studies science and math score) explain 48.9% of the variability of the dependent variable.  The Adjusted R Square measures the proportion of the variance in the response variable that can be explained by the predictor variables. In the table, the value of 0.479 indicates that the response variable can be perfectly explained by the predictor variables.  

 

Table 2: ANOVA

The ANOVA table above predicts whether the overall regression model is a good fit for the data. As shown in the table, the independent variable statistically significantly predicts the dependent variable F (4, 195) = 46.695, p<.05. This result implies that the regression model is a good fit for the data.

Table 3: Coefficients between the dependent and independent variables

 

When all other independent variables are maintained constant, unstandardized coefficients show how much the dependent variable varies with an independent variable. As shown in the table above, the unstandardized coefficient,  for math score is 0.389. This implies that a unit increase in math scores will cause an increase in science scores. Also, the coefficient for female is equal to -2.010. the p-value of 0.051 however suggests that the results is not statistically significant at the 0.05 significance level. Furthermore, a unit increase in social studies score, will increase the science score by 0.050. the p-value of 0.424 shows that there is no statistically significant effect of social studies score on science score. Finally, when there is a unit increase in the reading score, there will be a corresponding increase in the science score of 0.335. similarly, the pvalue of 0.000 shows that there is a statistically significant effect of reading score on science score.

Conclusion

In general, a multiple regression was run to predict science scores from math scores, females, reading scores and social studies scores. With the exception of female, social studies score, all variables are statistically significant at predict science score,  F(4, 195) = 46.695, p<.0005,  = .479.

References

Arayesh, M. B. (2015).­­­­­ Regression Analysis of Effective Factors on increasing Factors on trainer’s motivation of the Red Crescent Society (A Case Study, Ilam, Iran). Procedia-Social and Behavioral Sciences, 205, 536-541.

Kang, H., & Zhao, H. (2020, September). Description and Application Research of Multiple Regression Model Optimization Algorithm Based on Data Set Denoising. In Journal of Physics: Conference Series (Vol. 1631, No. 1, p. 012063). IOP Publishing.

Uyanık, G. K., & Güler, N. (2013). A study on multiple linear regression analysis. Procedia-Social and Behavioral Sciences, 106, 234-240.