# Understanding regression coefficient

Regression coefficient is a statistical measure of the average functional relationship between variables. Regression coefficient was first used in the estimation of height between fathers and sons. Regression coefficient is expressed in terms of unit of data. Additionally, regression coefficients can be classified as positive and negative, linear and non-linear and simple, partial, and multiple.

• Diastolic Blood Pressure (mmHg)
• Histograms and Boxplot Visualization

## Diastolic Blood Pressure (mmHg)  0:underweight; 1 normal; 2 overweight; 3: obese.

## Histograms and Boxplot Visualization

Diastolic Blood Pressure (mmHg) The histogram for diastolic blood pressure has a mound in the center and similar tapering to both the left and right, one indication of this shape is that the diastolic blood pressure is unimodal and normally distributed. The box plot shows that the diastolic blood pressure of subjects are normally distributed and reveals both lower and upper outliers in the diastolic blood pressure of subjects
Serum Cholesterol Level (mg/100ml) The distribution of the serum cholesterol level looks symmetric around the mean 225.4 and appears to fit the Normal Distribution well. The above boxplot reveals a normally distributed serum cholesterol level with some upper outliers
Subject’s Age in Years The histogram for the subject’s age in years has several mounds tapering to both the left and right; one indication of this shape is that the subject’s age in years is multimodal and fairly normal distributed. The box plot shows that subject’s age is fairly normal distributed and reveals both lower and upper outliers in diastolic blood pressure of subjects and that there are no outliers in the subject age.
The regression model to compare the mean DBP between males and females The resulting fitted model as the equation; The coefficients table gives us the coefficients of the independent variables in the regression model. The regression equation tells us that, holding the subject’s age constant, the diastolic blood pressure decreases by 2.302 when the subject is a female than when the subject is a male

Also, a one-unit increase in the age of the subject is associated with a 0.375 unit increase in diastolic blood pressure holding the gender of the subject is held constant.

The regression model to compare the mean DBP for BMI categories adjusting for age yrs and sex using “normal weight” The resulting regression equation is given by; The regression equation tells us that:
· A one-unit increase in the age of the subject is associated with a 0.289 unit increase in diastolic blood pressure holding other independent variables constant. The p-value for the subject age is less than 0.05 which indicate that the age has a significant effect on the subjects diastolic blood pressure
· Holding independent variables constant, the diastolic blood pressure decreases by 1.62 when the subject is a female than when the subject is a male. Also, the difference in average diastolic blood pressure between females and males was not statistically significant (p=0.108) after controlling for other variables.