# DABench Task 530 - Is there a correlation between the age of the passengers and the fare paid? How does this correlation differ among male and female passengers?

## Task Description

Is there a correlation between the age of the passengers and the fare paid? How does this correlation differ among male and female passengers?

## Concepts

Correlation Analysis, Distribution Analysis

## Data Description

Dataset file: `titanic_test.csv`

The data is available in the `train.csv` file in the public directory.

## Constraints

Calculate the Pearson correlation coefficient (r) to assess the strength and direction of the linear relationship between age and fare for male and female passengers separately. Assess the significance of the correlation using a two-tailed test with a significance level (alpha) of 0.05. Report the p-value associated with the correlation test. Consider the relationship to be linear if the p-value is less than 0.05 and the absolute value of r is greater than or equal to 0.5. Consider the relationship to be nonlinear if the p-value is less than 0.05 and the absolute value of r is less than 0.5. If the p-value is greater than or equal to 0.05, report that there is no significant correlation.

## Files

- `train.csv` - The training data
- `sample_submission.csv` - A sample submission file in the correct format

## Submission Format

Submit a single-row CSV with columns `id,answer`.

- `id`: always `530`
- `answer`: six key-value pairs separated by spaces: `@correlation_coefficient_male[<r_value>] @relationship_type_male[<relationship_type>] @relationship_type_female[<relationship_type>] @p_value_female[<p_value>] @correlation_coefficient_female[<r_value>] @p_value_male[<p_value>]`

`<r_value>` is between -1 and 1 (two decimals), `<p_value>` is between 0 and 1 (four decimals), and `<relationship_type>` is `linear`, `nonlinear`, or `none`.

## Evaluation

Submissions are evaluated on **exact match** with the ground truth answer (with tolerance of 0.01 for floating-point values).

## Goal

Provide the correct answer in the specified format.

## Difficulty Level

Hard
