Let's solve this in steps based on the tasks given:

1. Fit a simple linear regression model
   We have the data points for Advertising Cost (X) and Sales (Y). Using linear regression analysis, we will calculate the slope ($b$) and intercept ($a$) of the line $Y = a + bX$.

   Formula:

   • Slope $b = \frac{n(\sum XY) - (\sum X)(\sum Y)}{n(\sum X^2) - (\sum X)^2}$
   • Intercept $a = \frac{\sum Y - b(\sum X)}{n}$

2. Write the regression equation $Y = a + bX$
   After calculating $a$ and $b$ from the data, we substitute these values to get the equation.

3. Predict sales when advertising cost is $7,000
   Substitute $X = 7,000$ into the equation $Y = a + bX$ to find the predicted sales.

I'll calculate this and provide the results.import numpy as np import pandas as pd

Given data

advertising_cost = np.array([2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500]) sales = np.array([25000, 27500, 30000, 32000, 34500, 36000, 39000, 40500, 43000, 45000])

Number of data points

n = len(advertising_cost)

Calculating the necessary summations for slope (b) and intercept (a)

sum_x = np.sum(advertising_cost) sum_y = np.sum(sales) sum_xy = np.sum(advertising_cost * sales) sum_x2 = np.sum(advertising_cost ** 2)

Calculating slope (b) and intercept (a)

b = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x ** 2) a = (sum_y - b * sum_x) / n

The regression equation

regression_equation = f"Y = {a:.2f} + {b:.2f}X"

Prediction when advertising cost is $7,000

x_pred = 7000 y_pred = a + b * x_pred

regression_equation, y_pred('Y = 16524.24 + 4.41X', 47366.66666666667)('Y = 16524.24 + 4.41X', 47366.66666666667)success