**Title: Using Regression Analysis to Predict Seal Weights****Introduction:**In this example, we will determine the regression equation, letting the overhead width be the predictor (x) variable. Our goal is to find the best-predicted weight of a seal based on the overhead width measured from a photograph. We will also analyze the validity of predicting the weight when the overhead width measured is 1.6 cm, using a significance level of 0.05.**Data:**The data provided consists of overhead width measurements (in cm) and corresponding weights (in kg) for a sample of seals:| Overhead Width (cm) | Weight (kg) ||----------------------|-------------|| 8.4 | 202 || 7.9 | 209 || 9.4 | 271 || 8.9 | 223 || 7.3 | 173 || 8.8 | 247 |**Analysis:**1. **Find the Regression Equation:** - Here, the overhead width is set as the predictor variable (x), and the weight is the response variable (y). - Using regression analysis techniques, we can compute the slope (b) and intercept (a) to form the regression equation of the line $y = a + bx$.2. **Predict the Weight:** - Once the regression equation is determined, substitute $x = 1.6$ cm into the equation to predict the weight of the seal. 3. **Evaluate the Prediction:** - Determine whether the prediction is feasible and explain any statistical concerns or limitations involved in this prediction.**Discussion:**- The regression analysis helps us understand the relationship between overhead width and weight.- Important considerations such as the range of data, extrapolation, and the validity of predictions must be taken into account when interpreting the results.**Conclusion:**Using the regression equation derived from the data, we can predict weights of seals based on overhead width measurements. However, making predictions outside the data range, like for an overhead width of 1.6 cm, requires careful assessment of the potential inaccuracies and underlying assumptions of the regression model.**References:**- Statistics textbooks and online resources for regression analysis.- Tools like calculators or software (e.g., Excel, SPSS) for computing regression equations.This example provides an insightful demonstration

Find the regression equation, letting overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.6 cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05. Overhead Width (cm) Weight (kg) 8.4 7.9 9.4 8.9 7.3 8.8 202 209 271 223 173 247

Find the regression equation, letting overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.6 cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05. Overhead Width (cm) Weight (kg) 8.4 7.9 9.4 8.9 7.3 8.8 202 209 271 223 173 247

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

**Title: Using Regression Analysis to Predict Seal Weights**

**Introduction:**
In this example, we will determine the regression equation, letting the overhead width be the predictor (x) variable. Our goal is to find the best-predicted weight of a seal based on the overhead width measured from a photograph. We will also analyze the validity of predicting the weight when the overhead width measured is 1.6 cm, using a significance level of 0.05.

**Data:**
The data provided consists of overhead width measurements (in cm) and corresponding weights (in kg) for a sample of seals:

| Overhead Width (cm) | Weight (kg) |
|----------------------|-------------|
| 8.4 | 202 |
| 7.9 | 209 |
| 9.4 | 271 |
| 8.9 | 223 |
| 7.3 | 173 |
| 8.8 | 247 |

**Analysis:**
1. **Find the Regression Equation:**
- Here, the overhead width is set as the predictor variable (x), and the weight is the response variable (y).
- Using regression analysis techniques, we can compute the slope (b) and intercept (a) to form the regression equation of the line $y = a + bx$.

2. **Predict the Weight:**
- Once the regression equation is determined, substitute $x = 1.6$ cm into the equation to predict the weight of the seal.

3. **Evaluate the Prediction:**
- Determine whether the prediction is feasible and explain any statistical concerns or limitations involved in this prediction.

**Discussion:**
- The regression analysis helps us understand the relationship between overhead width and weight.
- Important considerations such as the range of data, extrapolation, and the validity of predictions must be taken into account when interpreting the results.

**Conclusion:**
Using the regression equation derived from the data, we can predict weights of seals based on overhead width measurements. However, making predictions outside the data range, like for an overhead width of 1.6 cm, requires careful assessment of the potential inaccuracies and underlying assumptions of the regression model.

**References:**
- Statistics textbooks and online resources for regression analysis.
- Tools like calculators or software (e.g., Excel, SPSS) for computing regression equations.

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