It seems that you've uploaded an image. Let me analyze the content for you. PIL import Image

Open the image to inspect its content

image_path = '/mnt/data/1733508398864ri6b7itb.jpg' image = Image.open(image_path)

Show the image to analyze it

image.show()I have displayed the image. Let me analyze its contents now to understand what it involves. Attempting to extract text from the image using OCR (Optical Character Recognition) import pytesseract

Use pytesseract to extract text from the image

text = pytesseract.image_to_string(image)

textThe image contains a table and instructions related to a linear regression problem. Here's the key information extracted from the image:

Problem Description:

• The table lists "Years since 1995" (denoted as $x$) and "New Cases" (denoted as $y$).
• You're asked to write the linear regression equation based on the given data, rounding the coefficients to the nearest hundredth.
• Then, you're required to estimate the calendar year when the number of new cases reaches 1282.

Extracted Data:

• Year 0 (1995): 1053 cases
• Year 1: 1059 cases
• Year 2: 1122 cases
• Year 3: 1156 cases
• Year 4: 1145 cases
• Year 5: 1194 cases

Next steps:

1. I will calculate the linear regression equation for this data.
2. Then, I'll estimate the year when the new cases reach 1282.

Let's proceed with the regression calculation and estimation. numpy as np from sklearn.linear_model import LinearRegression

Defining the data (x represents years since 1995, y represents new cases)

x_data = np.array([0, 1, 2, 3, 4, 5]).reshape(-1, 1) y_data = np.array([1053, 1059, 1122, 1156, 1145, 1194])

Creating a linear regression model and fitting it to the data

model = LinearRegression() model.fit(x_data, y_data)

Get the coefficients of the linear regression equation

slope = model.coef_[0] intercept = model.intercept_

Linear regression equation: y = mx + b, where m is the slope and b is the intercept

equation = f"y = {slope:.2f}x + {intercept:.2f}"

Estimate the year when new cases would reach 1282

target_y = 1282 estimated_x = (target_y - intercept) / slope # Solving for x when y = 1282 estimated_year = 1995 + estimated_x # Add the base year (1995) to estimate the calendar year

equation, estimated_yearThe linear regression equation that models the relationship between years since 1995 and the number of new cases is:

$y = 28.49x + 1050.29$

Where:

• $y$ is the number of new cases,
• $x$ is the number of years since 1995.

To estimate the calendar year when the number of new cases reaches 1282, we find that:

• The estimated year is 2003.13.

Thus, the number of new cases would reach approximately 1282 in the year 2003.

Would you like further details on the calculations or any other clarifications? Here's a list of related questions you might find useful:

1. How do you calculate the linear regression coefficients manually?
2. What is the significance of the slope in a linear regression model?
3. How can I interpret the intercept in a regression equation?
4. What are potential limitations of using linear regression for real-world data prediction?
5. How can I visualize this linear regression model on a graph?

Tip: Always check the residuals (differences between predicted and actual values) when applying linear regression, as they help determine how well the model fits the data.