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Stats 2 Extra Activity 3

Statistical Analysis Overview

Statistical Analysis Overview

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Very first, you have to do is to copy the data from the provided sheet. Then select any three numerical variables from the following options:

  • Current Ratio
  • Quick Ratio
  • Cash Ratio
  • P/E (Price to Earnings Ratio)
  • Earnings Yield
  • ROCE (Return on Capital Employed)
  • CASA (Current Account Savings Account Ratio)

For this activity, I have taken the Current Ratio, P/E Ratio, and Earnings Yield. Next, draw scatter plots for each pair of two numerical variables: X1 and X2, X2 and X3, and X1 and X3. After creating the scatter plots, write a few lines explaining the behavior observed in each plot.

Then, use Google Sheets to calculate the covariance using the formula =COVARIANCE.P(A2:A1001, B2:B1001) for each variable pair, and explain the results.

Similarly, calculate the mean and standard deviation in Google Sheets. Note that you cannot find the standard deviation directly; first, find the variance and then take the square root of it to get the standard deviation.

Chebyshev's inequality

For the next part, copy the code from this location and embed it into your Google Site. If you are utilizing a different dataset, ensure that you update the mean and standard deviation values in the HTML code accordingly.

Copy from here👇

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Chebyshev's Inequality</title>
    <style>
        body {
            font-size: 18px; /* Default font size for body text */
            line-height: 1.6; /* Increase line height for better readability */
        }
        h1 {
            font-size: 28px; /* Font size for main heading */
        }
        h2 {
            font-size: 24px; /* Font size for subheadings */
        }
        code {
            font-size: 20px; /* Font size for code snippets */
            background-color: #f4f4f4; /* Light background for code readability */
            padding: 2px 4px; /* Padding around code for spacing */
            border-radius: 4px; /* Rounded corners for code snippets */
        }
        strong {
            font-size: 20px; /* Font size for emphasized text */
        }
    </style>
</head>
<body>
<h1><u>Chebyshev's Inequality</u></h1> 
<p>According to Chebyshev's inequality, for any \( k > 1 \), the proportion of observations that lie within \( k \) standard deviations of the mean is at least (1-1/k^2).</p>

<h2>Current Ratio</h2>
<p>For the Current Ratio, if we choose <strong>k = 2</strong>:</p>
<ul>
    <li>The lower bound is: <br>
        <code>μ - 2σ = -0.424 - 2(1.005) = -2.434</code>
    </li>
    <li>The upper bound is: <br>
        <code>μ + 2σ = -0.424 + 2(1.005) = 1.586</code>
    </li>
</ul>
<p>Thus, we can say that at least <strong>1 - 1/2² = 0.75</strong> (or 75%) of the Current Ratio values will lie between -2.434 and 1.586.</p>

<h2>P/E Ratio</h2>
<p>For the P/E Ratio, if we choose <strong>k = 2</strong>:</p>
<ul>
    <li>The lower bound is: <br>
        <code>μ - 2σ = 0.017 - 2(1.410) = -2.803</code>
    </li>
    <li>The upper bound is: <br>
        <code>μ + 2σ = 0.017 + 2(1.410) = 2.837</code>
    </li>
</ul>
<p>Thus, we can say that at least <strong>1 - 1/2² = 0.75</strong> (or 75%) of the P/E Ratio values will lie between -2.803 and 2.837.</p>

<h2>Earnings Yield</h2>
<p>For the Earnings Yield, if we choose <strong>k = 2</strong>:</p>
<ul>
    <li>The lower bound is: <br>
        <code>μ - 2σ = 0.507 - 2(1.214) = -1.921</code>
    </li>
    <li>The upper bound is: <br>
        <code>μ + 2σ = 0.507 + 2(1.214) = 2.935</code>
    </li>
</ul>
<p>Thus, we can say that at least <strong>1 - 1/2² = 0.75</strong> (or 75%) of the Earnings Yield values will lie between -1.921 and 2.935.</p>

</body>
</html>

How to do peer review?

Peer Review Criteria

  1. Presence of Data and Analysis Document: Full marks will be awarded if the dataset provided in the activity is used, as the instructions specify utilizing data from the provided sheet. While the activity requests the use of Google Docs, the use of Google Sheets is also acceptable based on convenience.
  2. Presence of Scatter Plots and Interpretation: Full marks will be given only if all three scatter plots are included, along with brief explanations for each plot.
  3. Computation of Covariance and Interpretation of Results: Full marks will be assigned if covariance is calculated for all three pairs of variables, accompanied by proper explanations of the results. Any missing computations will result in reduced marks.
  4. Calculations of Mean and Variances for Each Variable and Interpretation: Similar to covariance, full marks will be granted only if the mean and standard deviation for all three variables are calculated and properly interpreted.
  5. Lower and Upper Bounds and Their Interpretations: Lastly, check for the inclusion of lower and upper bounds calculated using the mean and standard deviation obtained earlier, along with their interpretations according to Chebyshev's inequality.

If you select Exemplary, it means you are giving full marks for that part.

Here is the link https://docs.google.com/spreadsheets/d/12xUKTYYBXXH8OTpfht-M0wYu1cKhW2x49_oWT0hYmg4/edit?usp=sharing for the data sheet.

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