Are there additional factors (other than age) that would have an impact on the results? Share those factors and how would your test impact?
Magnesium levels are one of the variables that affect the amount of Urea among patients. . Compared to patients with high magnesium levels , those with low magnesium levels have significantly lower levels of urea , uric acid and potassium (Lu et al., 2020). Other variables that affect urea levels include high levels of Body mass index and creatinine as well as suffering fatty liver.
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The model for multiple linear regression is as given below;
yi=β0+β1xi1+β2xi2+...+βpxip+ϵ
Whereby;
yi=dependent variable xi=explanatory variables β0=y-intercept (constant term) βp=slope coefficients for each explanatory variable ϵ=the model’s error term (also known as the residuals) Evaluation of Impact of Explanatory Variables in Multiple Regression Model
In the assessment of the impact, we will use the multiple linear regression models with the amount of urea acting as the dependent variable. The explanatory variables outlined above predict the amount of urea among patients. Each of the explanatory variables can be assessed against the outcome to ascertain the amount of variability explained by each of them when the rest are controlled for. The importance of each factor can be ascertained by the following procedures.
Evaluating the Multiple Regression
It starts with the testing the multiple linear regression assumptions.
The assumptions that must be checked are as follows;
There should be a linear relationship between the outcome/dependent variables and the independent variables.
The model residuals must follow a normal distribution.
There should be homogeneity of variance of the subpopulation of the fitted values.
The subpopulations of the fitted values should be independent from one observation of the predicator variable to the other.
The multiple regression coefficient of determination is one of the statistics to consider whether the full model is suitable in explaining variability of the dependent variable. In testing hypothesis for the coefficient of determination, the null hypothesis states that neither of the model coefficients has a linear relationship with the dependent variable. The alternative hypothesis states that at least one of the model coefficients is linearly related with the dependent variable.
The decision whether to reject the model or not is based on the value obtained from running a regression analysis using a statistical software for instance SPSS or Stata. A p-value less than the cut-off at 95% level of significance should be able to qualify the model as adequate in explaining variability in amount of urea within a patient. The coefficient of determination normally increases with addition of more predictor variables.
Partial regression coefficients have to be ascertained for one to determine the impact of each variable on the dependent variable. The independent variable that has a higher partial regression coefficient has greater impact on the variability of the dependent variable in this case urea amount in a patient (Berwick et al., 2003).
The regression coefficients show the significance of the individual explanatory variables in the model while the partial regression coefficients can be used to calculate the partial coefficient of determination. The partial coefficients of determination of each of the independent variables show the proportion of variability in a mount of urea explained by each of the independent variables controlling for
Based on the result what is the proposed next step from a business or patient care standpoint?
In modeling the variability of amount of urea among patients, it is important to settle on explanatory variables with the highest impact. These are variables with the highest partial coefficient of determination. Among these variables, cost implications and ease of data collection can be considered to settle on the variables that meet the threshold of cheaper means of obtaining data as well as greater impact on the response variable, dependent (amount of urea).
References
Bewick, V., Cheek, L., & Ball, J. (2003). Correlation and regression. Statistics review 7. Critical Care , 7 (6): 451–459. doi: 10.1186/cc2401 .
Lu, C., Wang, Y., Wang, D., Nie, L., Zhang, Y., Lei, Q., Xiong, J., & Zhao, J. (2020). Hypomagnesemia and short-term mortality in elderly maintenance hemodialysis patients. Kidney Dis (Basel), 6( 2):109-118. doi: 10.1159/000504601
