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https://r2.erweima.ai/mathbot/image/1725990347701ia43llnr.jpg

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Let's go step by step through the images you uploaded to solve the problems.

### First Problem: **Polinomic Regression Models**

From the first image, we have to determine two algebraic models, one of degree 1 (linear) and one of degree 3, that best fit the given data on product availability (stock) over time.

The data is:

| Días (x) | Stock (y) |
|----------|-----------|
| 6        | 3900      |
| 9        | 2400      |
| 18       | 1600      |
| 23       | 700       |
| 29       | 100       |

#### a) **Linear Model (Polinomic of Degree 1)**

We need to find the best fit for the linear equation of the form:

\[
f(x) = ax + b
\]

Let's calculate this using least squares regression for the data points.

#### b) **Cubic Model (Polinomic of Degree 3)**

Similarly, for the cubic polynomial, we need an equation of the form:

\[
g(x) = ax^3 + bx^2 + cx + d
\]

We will fit this cubic polynomial to the given data points.

#### Let me calculate both models.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like, I can guide you through the manual steps to solve the problem or attempt other sections of the exercise! Let me know how you'd like to proceed. 

Here are some questions you could explore:

1. What is the method to find the linear regression formula?
2. How do you calculate the coefficients of a polynomial of degree 3 manually?
3. How can we use least squares for polynomial fitting?
4. What role does the data's distribution play in choosing a polynomial degree?
5. What are the steps to predict stock availability at a given time?

**Tip:** For polynomial regression, higher-degree polynomials may better fit the data but risk overfitting, so balance is key.

Learn how to use polynomial regression models to predict product availability in a hypermarket, based on stock data over time. This problem involves creating a linear and cubic polynomial fit for product stock and estimating product shortage days. Suitable for university-level students.

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