Each part of a regression has some meaning and needs to be interpreted correctly. Here are two regression models:
Diabetes (1 unit) = 1.3 + 2.4 (BMI) + 2.3 (family history diabetes) + 1.7 (gender) + 1.4 (age) + 1.7 (race) + 2.6 (income) + 3.4 (height), p<0.05
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Allergies = 4.5 + 3.8 (Family History Allergies) + 2.1 (gender) + 1.4 (age) + 0.8 (race) + 1.5 (weight), p<0.05
In the first regression model, the dependent variable is diabetes, which depends on the predictor variables such as BMI, family history of diabetes, gender, age, race, income and height. The level of impact of each independent variable can be obtained by looking at their respective coefficients.
The first coefficient is that of BMI. The coefficient means that a unit increase in BMI of an individual will result in 2.4 unit increase in the units of diabetes. The coefficient of family history of diabetes means that having a family history of diabetes results in 2.3 units increase in diabetes. The coefficient of gender means that the gender that is numerically represented by 1 increases the units of diabetes by 1.7 units. Similarly, the race that is numerically represented by 1 increases the units of diabetes by 1.7 units. Moreover, a unit increase in age, income, and height would result in an increase of diabetes units by 1.4, 2.6, and 3.4 respectively.
Notably, diabetes and all the independent variables have positive correlation since the sign of the coefficients are positive, and thus the effect of the predictor variables on the dependent variable is positive (increasing). Furthermore, the p-value of the model is less than 0.05, which means that the model is statistically significant and can be used in predicting the units of diabetes.
In the second regression model, the dependent variable is allergies, which depends on the predictor variables such as family history of allergies, gender, age, race, and weight. The level of impact of each independent variable can be obtained by looking at their respective coefficients.
The first coefficient is that of family history of allergies. The coefficient means that having a family history of allergies results in 3.8 units increase of allergies. The coefficient of gender means that the gender that is numerically represented by 1 increases the units of allergies by 2.1 units. Similarly, the race that is numerically represented by 1 increases the units of allergies by 0.8 units. Moreover, a unit increase height would result in an increase in allergies units by 1.5.
Notably, allergies and all the independent variables have positive correlation since the sign of the coefficients are positive, and thus the effect of the predictor variables on the dependent variable is positive (increasing). Furthermore, the p-value of the model is less than 0.05, which means that the model is statistically significant and can be used in predicting the units of allergies.
A confounding variable is a variable that has an impact on the dependent and the independent variable (Cho, 2016) . The coefficients of the explanatory variables can be used to identify cofounders. In the first model, potential confounders are age, gender, and race. Their effects on diabetes are low as compared to other predictor variables. Also, in the second model, the potential confounders are age, gender, and race since they have minimum impact on allergies as compared to other factors.
Matching of potential confounders helps in controlling complex variables but can be time-consuming. Including the potential confounders in the regression model help to improve the model and provide an alternative explanation for the association between them and the variable being predicted (Khademi, 2016) . However, they can make the model insignificant due to the possible difference between the groups represented by the variables.
References
Cho, H. (2016). The analysis of multivariate longitudinal data using multivariate marginal models. Journal of Multivariate Analysis , 143 , 481-491. doi: 10.1016/j.jmva.2015.10.012
Khademi, A. (2016). Applied Univariate, Bivariate, and Multivariate Statistics. Journal of Statistical Software , 72 (Book Review 2). doi: 10.18637/jss.v072.b02
