Here we predict the weight of a man from his height using linear regression from the following data in the table for men:

We would like to estimate the weight of a man given that his height is 172cm.

Analysis using R:

In the previous example Fahrenheit and Celsius conversion, the data fitted the linear model perfectly. Thus we could perform even a simple mathematical analysis (solving basic equations) to gain the conversion formula. Most of the data in the realworld does not fit a model perfectly. For such an analysis, it is good to find the model that fits the given data with the minimal error. We use R do find such a linear model.

Input:

We put the data from the table above into the vectors and try to fit the linear model.

# source_code/6/weight_prediction.r
men = data.frame( 
     height = c(180,174,184,168,178), weight = c(75,71,83,63,70) 
) 
model = lm(weight ~ height, data = men)
print(model) 

Output:

$ Rscript weight_prediction.r
Call:
lm(formula = weight ~ height, data = men)
Coefficients: (Intercept)     height
                 -127.688      1.132

Thus the formula expressing the linear relationship between the weight and the height is as follows: weight=1.132*height-127.688. Therefore, we estimate that the man with the height of 172cm would have the weight 1.132*172-127.688=67.016 kg.