Suppose that we have a dataset of heights and weights for 100 adults. We fit a linear regression and print the coefficients:

model = sm.OLS.from_formula('weight ~ height', data = body_measurements)
results = model.fit()
print(results.params)

Output:

Intercept   -21.67
height        0.50
dtype: float64

This regression allows us to predict the weight of an adult if we know their height. To make a prediction, we need to plug in the intercept and slope to our equation for a line. The equation is:

$weight = 0.50*height - 21.67$

To make a prediction, we can plug in any height. For example, we can calculate that the expected weight for a 160cm tall person is 58.33kg:

$weight = 0.50*160-21.67 = 58.33$

In python, we can calculate this by plugging in values or by accessing the intercept and slope from results.params using their indices (0 and 1, respectively):

print(0.50 * 160 - 21.67) 
# Output: 58.33

# OR:

print(results.params[1]*160 + results.params[0])
# Output: 58.33

We can also do this calculation using the .predict() method on the fitted model. To predict the weight of a 160 cm tall person, we need to first create a new dataset with height equal to 160 as shown below:

newdata = {"height":[160]}
print(results.predict(newdata))

Output:

0      58.33
dtype: float64

Note that we get the same result (58.33) as with the other methods; however, it is returned as a data frame.