https://file.aiquickdraw.com/mathbot/file/173312055127383i0hahl.jpg


import numpy as np

# Data extracted from the table in the image
data_with_outlier = {
    "x": [48, 68.5, 49.4, 62.4, 66.1, 80.5, 69.8, 77.6, 50.5, 82.2, 42.4, 85.1, 72, 74.9, 213.2],
    "y": [667, -539, 112.7, 423.9, -412.3, -380.3, -468.7, 694.5, 13, 765.5, -854.6, -198.5, -517.3, 604.6, 5625.8]
}

data_without_outlier = {
    "x": [48, 68.5, 49.4, 62.4, 66.1, 80.5, 69.8, 77.6, 50.5, 82.2, 42.4, 85.1, 72, 74.9],
    "y": [667, -539, 112.7, 423.9, -412.3, -380.3, -468.7, 694.5, 13, 765.5, -854.6, -198.5, -517.3, 604.6]
}

# Convert to DataFrame
df_with_outlier = pd.DataFrame(data_with_outlier)
df_without_outlier = pd.DataFrame(data_without_outlier)

# Compute correlation coefficients
corr_with_outlier = df_with_outlier["x"].corr(df_with_outlier["y"])
corr_without_outlier = df_without_outlier["x"].corr(df_without_outlierThe correlation coefficients are as follows:

- **With the outlier** (\( r_w \)): **0.903** (rounded to three decimal places)
- **Without the outlier** (\( r_{wo} \)): **0.149** (rounded to three decimal places)

Let me know if you have questions or want further analysis!

Here are five related questions to explore:
1. How does the presence of an outlier impact the correlation coefficient in general?
2. Can we visualize the data points to see the impact of the outlier?
3. What statistical methods can be used to detect outliers in data sets?
4. Is it always appropriate to remove outliers, or are there cases where they should be retained?
5. How does the correlation coefficient influence regression analysis?

**Tip:** Always check for and address outliers in your data when performing statistical analyses, as they can significantly skew results.

What is the correlation coefficient with the outlier and without the outlier for the given bivariate data set?

Calculate the correlation coefficient for a given bivariate data set both with and without an outlier. Learn how outliers impact statistical relationships, with detailed analysis and solution steps. Suitable for high school and college-level statistics.

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