The selected data set is for body performance obtained from https://www.kaggle.com/datasets/kukuroo3/body-performance-dataLinks to an external site.. It entails various variables such as age, gender, height in cm, weight in kg, body fat percentage, diastolic blood pressure, systolic blood pressure and performance on exercises like grip force, sit ups etc. The variables I chose to analyze are weight of individuals with their minimum systolic blood pressures. The explanatory variable, x in this case is weight while the response variable, y is minimum systolic blood pressure of each person.

I would expect the two variables to have a positive correlation. Previous research on weight and systolic blood pressure denote a positive association between the variables. Increased body weight results to increased blood pressure while a reduced weight leads to improved blood pressure. According to a study done in the Hematology and Internal Medicine Polyclinics on sickle celled patients, their average body weight, which was lower than that of individuals in the control group had corresponding lower blood pressure values (Helvaci, Yaprak, Abyad, & Pocock, 2020). For instance, the patients had an average body weight of 57.8 kg with corresponding average systolic blood pressure of 113.3 mmHg, while the control group had a mean weight of 71.6 kg with a matching systolic blood pressure of 118.8 mmHg (Helvaci et al., 2020). Therefore, the variables should be positively correlated.

From the data used, the variables have a weak positive correlation. The obtained coefficient r of 0.3414 is closer to zero than 1 thus categorized as weak. The coefficient r² of 0.1165 signifies that about 11.65% of variations in systolic blood pressure values can be accounted for by changes in body weight values in the dataset.

The regression equation will be: Systolic blood pressure (Y) = 0.4176*Body Weight(X) + 102.09, where 0.4176 is the slope and 102.09 the intercept. Suppose we want to predict the systolic blood pressure for an individual with a body weight of 60.50 kilograms, it will be: Y = 0.4176*60.50 + 102.09 = 127.4. Thus, according to the obtained model, the minimum systolic blood pressure of a person weighing 60.50 kilograms is 127 mmHg.

How does extrapolation apply here?