Question 1
In hierarchical multiple regression, variables are added into the model in different blocks. In this case, the dependent variable is the memory function in elderly people. The research is aimed at finding the nature of the association between memory function and social contact. Two blocks will be used in this regression analysis. Social contact is the primary independent variable hence block 1 will include social contact and memory function among healthy elderly people. The two variables will be regressed to obtain a model. After regression, the R-Squared of the model is checked to determine the changes in Y (memory function) that are explained by the changes in X (social contact) (Cramer, 2003).
The second block will contain the age of the elderly people. This will be added as an independent variable to the first model to obtain a new model. The new R Square is noted. The second block will be for the independent variable, education. The levels of education are added to the model, and the new R Square is studied (Cramer, 2003). More variables can be added to the model.
Question 2
In hierarchical regression, variables are entered in blocks, and the new model is studied to determine if the subsequent blocks improve the model. One of the reliability measures of a model is its coefficient of determination (R Squared). A model is more reliable when the R-Squared is higher than when it is lower. The coefficient of determination can be increased by adding more independent variables to the model such that the percentage of changes in Y explained by the changes in independent variables is high (Lomax & Hahs-Vaughn, 2012).
When the first variables entered in block 1 are regressed, the R-Squared is noted. When another variable is added to the model, the R-Squared of the new model is noted and compared with the original R Squared. For instance, if the model for Y(X1) has an R-Squared of 0.75 and that of Y(X1, X2) is 0.81, then we can conclude that the introduction of variable X2 to the original model improves its coefficient of determination by 0.06. A model is said to have improved if the value of R-Squared increases. Therefore, through hierarchical multiple regression, we can determine if a variable in the subsequent blocks improves the model.
Question 3
Zero-order correlations are correlations between two variables. For instance, in the study of the relationship between two variables X and Y, the correlation between the two is a zero-order correlation (Healey, 2015, p. 370). They involve only two variables.
Partial correlations are used to determine the correlation coefficient between two variables while controlling for one or more variables (Norris, Qureshi, & Howitt, 2014, p. 284). For instance, when studying the relationship between X and Y while holding variable Z constant for both X and Y to eliminate the impact of Z on the two variables.
Semi-partial correlation involves computing the correlation coefficient between two variables X and Y while holding Z constant for only X or Y and not for both. Unlike the partial correlation, the control variable is held constant for only one of the two variables.
When studying the unique variance in one variable as explained by another variable when controlling for other variables, we use the partial correlation (Norris, Qureshi, & Howitt, 2014, p. 284). Only partial correlation can be used to determine the unique relationship between any two variables. All the other variables must be controlled for both the dependent and the independent variables. If the control variables are only held constant for only one variable (X or Y), then the relationship cannot be unique. It will be affected by the influence of the control variables on either the dependent or independent variable.
References
Cramer, D. (2003). Advanced quantitative data analysis. Maidenhead, Berkshire, England:
Open University Press.
Healey, J. (2015). The Essentials of Statistics: A Tool for Social Research (4th ed.). New
York: Cengage Learning.
Lomax, R. & Hahs-Vaughn, D. (2012). An introduction to statistical concepts. New York:
Routledge.
Norris, G., Qureshi, F., & Howitt, D. (2014). Introduction to Statistics with SPSS for Social
Science. Florence: Taylor and Francis.
