What is the value of n? What is the value of ΣX? What is the value of ΣX2? What is the value of ΣXY? What is the value of ΣY2? What is the value of r?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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  • What is the value of n?
  • What is the value of ΣX?
  • What is the value of ΣX2?
  • What is the value of ΣXY?
  • What is the value of ΣY2?
  • What is the value of r?
**Instructions:**

Use the following formula to calculate the correlation coefficient \( r \):

\[
r = \frac{n\Sigma xy - \Sigma x \Sigma y}{\sqrt{\left[n\Sigma x^2 - (\Sigma x)^2\right] \left[n\Sigma y^2 - (\Sigma y)^2\right]}}
\]

Or, alternatively, use these formulas:

\[
r = \frac{SP}{\sqrt{SS_x SS_y}}
\]

Where:
- \( SP = \Sigma xy - \frac{\Sigma x \Sigma y}{n} \)
- \( SS = \Sigma x^2 - \frac{(\Sigma x)^2}{n} \)

You will need to calculate \( SS \) for both \( X \) and \( Y \).

**Table to Fill:**

Calculate the necessary values and fill in the table below to use the equations above to calculate \( r \).

| Subject   | X | X² | XY | Y | Y² |
|-----------|---|----|----|---|----|
| Mercutio  | 2 |    |    | 0 |    |
| Juliet    | 5 |    |    | 8 |    |
| Romeo     | 4 |    |    | 5 |    |
| Nurse     | 3 |    |    | 6 |    |
| Prospero  | 3 |    |    | 4 |    |
| \(\Sigma\) |   | \(\Sigma\) | \(\Sigma\) |   | \(\Sigma\) |

Fill in the squares for \( X^2, XY, \) and \( Y^2 \), and calculate the sums (\(\Sigma\)) needed for the equations.
Transcribed Image Text:**Instructions:** Use the following formula to calculate the correlation coefficient \( r \): \[ r = \frac{n\Sigma xy - \Sigma x \Sigma y}{\sqrt{\left[n\Sigma x^2 - (\Sigma x)^2\right] \left[n\Sigma y^2 - (\Sigma y)^2\right]}} \] Or, alternatively, use these formulas: \[ r = \frac{SP}{\sqrt{SS_x SS_y}} \] Where: - \( SP = \Sigma xy - \frac{\Sigma x \Sigma y}{n} \) - \( SS = \Sigma x^2 - \frac{(\Sigma x)^2}{n} \) You will need to calculate \( SS \) for both \( X \) and \( Y \). **Table to Fill:** Calculate the necessary values and fill in the table below to use the equations above to calculate \( r \). | Subject | X | X² | XY | Y | Y² | |-----------|---|----|----|---|----| | Mercutio | 2 | | | 0 | | | Juliet | 5 | | | 8 | | | Romeo | 4 | | | 5 | | | Nurse | 3 | | | 6 | | | Prospero | 3 | | | 4 | | | \(\Sigma\) | | \(\Sigma\) | \(\Sigma\) | | \(\Sigma\) | Fill in the squares for \( X^2, XY, \) and \( Y^2 \), and calculate the sums (\(\Sigma\)) needed for the equations.
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