Find The Intercept

The intercept helps refine the function’s ability to predict Calorie_Burnage.

It represents the point where the diagonal line would cross the y-axis if extended.

The intercept is the value of y when x equals zero.

In this case, when the average pulse (x) is zero, the calorie burnage (y) is 80, making the intercept 80.

While the intercept may not always have a practical meaning, it is essential for completing the function’s predictive accuracy.

For instance, in some cases, the intercept may have a practical interpretation:

Predicting next year’s revenue using marketing expenditure (even with zero marketing spend, a company may still generate some revenue).
Estimating fuel consumption with speed (a car still uses fuel even when idling at 0 mph).

Find the Slope and Intercept Using Python

The np.polyfit() function returns both the slope and the intercept.

By using the following code, we can obtain both the slope and intercept from the function.

Example

import pandas as pd
import numpy as np

health_data = pd.read_csv(“data.csv”, header=0, sep=“,”)

x = health_data[“Average_Pulse”]
y = health_data[“Calorie_Burnage”]
slope_intercept = np.polyfit(x,y,1)

print(slope_intercept)

Example Explained:

Isolate the variables Average_Pulse (x) and Calorie_Burnage (y) from the health_data.
Call the np.polyfit() function.
The last parameter of the function indicates the degree of the function, which in this case is “1” (for a linear function).

We have now calculated the slope (2) and the intercept (80). The mathematical function to predict Calorie_Burnage is:

$\text{Calorie_Burnage} = 2 \times \text{Average_Pulse} + 80$

f(x) = 2x + 80

Task:

To predict calorie burnage when the average pulse is 135, we substitute the input $x = 135$ into the equation, remembering that the intercept (80) remains constant:

$\text{Calorie_Burnage} = 2 \times 135 + 80$

f(135) = 2 * 135 + 80 = 350

If the average pulse is 135, the predicted calorie burnage is 350.