For the following scores,| X | Y ||----|----|| 7 | 6 || 9 | 6 || 6 | 3 || 12 | 5 || 9 | 6 || 5 | 4 |Using the Graphs tool below, sketch a scatter plot showing the six data points.**Scatter plot explanation:**The scatter plot displays points on a two-dimensional graph, representing the relationship between the X and Y values. - The X-axis ranges from 5 to 12.- The Y-axis ranges from 3 to 7.- Six points are plotted corresponding to the pairs of X and Y values given in the table.- The points are distributed such that some X values have the same Y values, resulting in overlapping on the Y-axis. Specifically, the points for (7, 6) and (9, 6) appear close together. The image contains a scatter plot and elements related to Pearson correlation analysis, intended for educational purposes.### Scatter Plot Description:- The graph has points scattered around a trend line. The line has a direction that shows it is sloping downwards to the left. - The x-axis is labeled as "X" with values ranging from 0 to 14.- The y-axis is labeled as "Y" with values ranging from 0 to 14.### Estimating Pearson Correlation:- The task is to estimate the value of the Pearson correlation by observing the scatter plot.- Options provided are: 1. The correlation is small but positive; around 0.8 to 1.0. 2. The correlation is small but positive; around 0.4 to 0.6. 3. The correlation is small but negative; around -0.4 to -0.7.### Table for Calculating Pearson Correlation:- There is a table with empty fields for calculations related to Pearson correlation: - ΣX² (Sum of X squared) - ΣY² (Sum of Y squared) - ΣXY (Sum of the product of X and Y) - SSₓ (Sum of squares of X) - SSᵧ (Sum of squares of Y) - SP (Sum of products)### Compute the Pearson Correlation:- There is a blank space to compute and write down the Pearson correlation value.This educational resource helps students learn how to visually estimate and calculate Pearson correlation from given data.

Given X 7 9 6 12 9 5 Y 6 6 3 5 6 4

2 4 8 10 12 14 The scatter plot shows points widely scattered around a line sloping down to the left v Just looking at the scatter plot, estimate the value of the Pearson correlation. The correlation is small but positive; around 0.8 to 1.0. O The correlation is small but positive; around 0.4 to 0.6. The correlation is small but negative; around -0.4 to -0.7. Complete the following table. ΣΧ2 ΣΥ2 ΣΧΥ SSx SSy SP Compute the Pearson correlation. Pearson correlation =

2 4 8 10 12 14 The scatter plot shows points widely scattered around a line sloping down to the left v Just looking at the scatter plot, estimate the value of the Pearson correlation. The correlation is small but positive; around 0.8 to 1.0. O The correlation is small but positive; around 0.4 to 0.6. The correlation is small but negative; around -0.4 to -0.7. Complete the following table. ΣΧ2 ΣΥ2 ΣΧΥ SSx SSy SP Compute the Pearson correlation. Pearson correlation =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

For the following scores,

| X | Y |
|----|----|
| 7 | 6 |
| 9 | 6 |
| 6 | 3 |
| 12 | 5 |
| 9 | 6 |
| 5 | 4 |

Using the Graphs tool below, sketch a scatter plot showing the six data points.

**Scatter plot explanation:**

The scatter plot displays points on a two-dimensional graph, representing the relationship between the X and Y values.

- The X-axis ranges from 5 to 12.
- The Y-axis ranges from 3 to 7.
- Six points are plotted corresponding to the pairs of X and Y values given in the table.
- The points are distributed such that some X values have the same Y values, resulting in overlapping on the Y-axis. Specifically, the points for (7, 6) and (9, 6) appear close together.

The image contains a scatter plot and elements related to Pearson correlation analysis, intended for educational purposes.

### Scatter Plot Description:
- The graph has points scattered around a trend line. The line has a direction that shows it is sloping downwards to the left.
- The x-axis is labeled as "X" with values ranging from 0 to 14.
- The y-axis is labeled as "Y" with values ranging from 0 to 14.

### Estimating Pearson Correlation:
- The task is to estimate the value of the Pearson correlation by observing the scatter plot.
- Options provided are:
1. The correlation is small but positive; around 0.8 to 1.0.
2. The correlation is small but positive; around 0.4 to 0.6.
3. The correlation is small but negative; around -0.4 to -0.7.

### Table for Calculating Pearson Correlation:
- There is a table with empty fields for calculations related to Pearson correlation:
- ΣX² (Sum of X squared)
- ΣY² (Sum of Y squared)
- ΣXY (Sum of the product of X and Y)
- SSₓ (Sum of squares of X)
- SSᵧ (Sum of squares of Y)
- SP (Sum of products)

### Compute the Pearson Correlation:
- There is a blank space to compute and write down the Pearson correlation value.

This educational resource helps students learn how to visually estimate and calculate Pearson correlation from given data.

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