5. For the following scores, Y 4 compatational 1 confuse the 1 4 nor
![**Problem 5: Analysis of Data Correlation**
Given the following scores:
| X | Y |
|---|---|
| 4 | 0 |
| 1 | 5 |
| 1 | 0 |
| 4 | 5 |
Tasks:
a. **Sketch a Scatter Plot and Estimate the Pearson Correlation:**
- Create a graph with the X values on the horizontal axis and the Y values on the vertical axis.
- Plot the given pairs (4,0), (1,5), (1,0), and (4,5) as points on the graph.
- Visually estimate the strength and direction of the correlation between X and Y.
b. **Compute the Pearson Correlation:**
- Use the Pearson correlation coefficient formula to calculate the exact correlation:
\[
r = \frac{n(\sum{XY}) - (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} - (\sum{X})^2][n\sum{Y^2} - (\sum{Y})^2]}}
\]
- Where \( n \) is the number of pairs, \(\sum{XY}\) is the sum of the products of paired scores, \(\sum{X}\) and \(\sum{Y}\) are the sums of X and Y scores, \(\sum{X^2}\) and \(\sum{Y^2}\) are the sums of squared X and Y scores.
The goal is to evaluate how strongly and in what direction X and Y are related based on the data provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d2b439b-9921-445d-b564-5f8ee77e0431%2F9cbb3cec-8abf-403b-b7f3-557912858aca%2Flusbixn_processed.jpeg&w=3840&q=75)
Given the following scores,
| X | Y |
| 4 | 0 |
| 1 | 5 |
| 1 | 0 |
| 4 | 5 |
(a) To sketch a scatter plot and estimate the Pearson Correlation:
Scatter plot explains the association or correlation between two variables, If the dots in the plot are scattered randomly there is no association between the two variables. The range of the correlation or association is -1 and +1 inclusively.
The procedure to draw a scatterplot using MS-Excel is shown below:
- Enter the data in the Excel spreadsheet.
- Select the data, go to 'insert' from menu bar.
- Under chart types, select scatter plot
- Click ok.
The output of scatter plot from MS-Excel is given below:
The scatter plot shows that the points are randomly scattered, there is no slopping towards the right or the left which means there is no association or relationship between the two variables. AS one variable increases, there is no tendency in the other variable to either increase or decrease.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
