**Exercise 6: Analyzing the Dataset**For the following data:a. **Objective:** Find the regression equation for predicting $ Y $ from $ X $.b. **Objective:** Calculate the Pearson correlation for these data. Use $ r^2 $ and $ SS_Y $ to compute $ SS_{\text{residual}} $ and the standard error of estimate for the equation.| $ X $ | $ Y $ ||-------|-------|| 3 | 3 || 6 | 9 || 5 | 8 || 4 | 3 || 7 | 10 || 5 | 9 |In this exercise, the learner will engage with statistical methods to derive critical insights from the dataset. The goal is to understand the relationship between the variables $ X $ and $ Y $ through the construction and analysis of a regression model. Students will also calculate the strength of this relationship using the Pearson correlation coefficient and explore variance calculations.

Given: The data is shown below as,

For the following data: a. Find the regression equation for predicting Y from X. b. Calculate the Pearson correlation for these data. Use r2 and SS_Y to compute SSresidual and the standard error of estimate for the equation. Y 3 3 4 3 7 10 5 9.

For the following data: a. Find the regression equation for predicting Y from X. b. Calculate the Pearson correlation for these data. Use r2 and SS_Y to compute SSresidual and the standard error of estimate for the equation. Y 3 3 4 3 7 10 5 9.

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

**Exercise 6: Analyzing the Dataset**

For the following data:

a. **Objective:** Find the regression equation for predicting $ Y $ from $ X $.

b. **Objective:** Calculate the Pearson correlation for these data. Use $ r^2 $ and $ SS_Y $ to compute $ SS_{\text{residual}} $ and the standard error of estimate for the equation.

| $ X $ | $ Y $ |
|-------|-------|
| 3 | 3 |
| 6 | 9 |
| 5 | 8 |
| 4 | 3 |
| 7 | 10 |
| 5 | 9 |

In this exercise, the learner will engage with statistical methods to derive critical insights from the dataset. The goal is to understand the relationship between the variables $ X $ and $ Y $ through the construction and analysis of a regression model. Students will also calculate the strength of this relationship using the Pearson correlation coefficient and explore variance calculations.

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