Find the regression equation that best fits **Exercise 18: Constructing a Scatterplot and Identifying the Best-Fit Model****Objective:**The task is to construct a scatterplot based on the given data and determine the mathematical model that best fits this data. The model should be chosen from linear, quadratic, logarithmic, exponential, and power models. It is important to note that the model should apply only within the scope of the provided data.**Instructions:**1. Use a calculator or computer software to generate a scatterplot for the given data.2. Fit multiple models to the data and compare their effectiveness using the regression equations provided.3. Evaluate the fit of each model by comparing the values of $ R^2 $.**Data:**| $ x $ | 1 | 4 | 5 | 9 | 11 | 16 ||---------|----|----|----|----|----|----|| $ y $ | 9 | 13 | 25 | 27 | 31 | 46 |**Potential Regression Models:**1. **Linear Model:** \[ y = 7.04 + 2.36x \]2. **Exponential Model:** \[ y = 8.14x^{0.58} \]3. **Logarithmic Model:** \[ y = 4.40 + 12.02 \ln x \]4. **Quadratic Model:** \[ y = 0.01x^2 - 2.19x + 7.53 \]**Steps to Complete:**1. **Scatterplot:** - Plot the given data points $(x, y)$ on a graph. - Observe the trend of the points to get a preliminary idea of which model might fit well.2. **Model Fitting:** - Fit the linear, exponential, logarithmic, and quadratic models to the data. - Use software tools to obtain the regression equations and the $ R^2 $ values.3. **Comparison:** - Analyze which model provides the highest $ R^2 $ value, indicating the best fit. - Confirm that the best-fit model logically aligns with the data's trend.By successfully completing this exercise, students will gain experience in data analysis and model fitting,

8. Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R. x1 4 5 9 11 16 v9 13 25 27 31 46 Oy=7.04 + 2.36x Oy=8.14x° 58 Ov3D4,40+ 12.02 In x V3D0.01x-+ 2.19x + 7,53

8. Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R. x1 4 5 9 11 16 v9 13 25 27 31 46 Oy=7.04 + 2.36x Oy=8.14x° 58 Ov3D4,40+ 12.02 In x V3D0.01x-+ 2.19x + 7,53

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

Find the regression equation that best fits

**Exercise 18: Constructing a Scatterplot and Identifying the Best-Fit Model**

**Objective:**
The task is to construct a scatterplot based on the given data and determine the mathematical model that best fits this data. The model should be chosen from linear, quadratic, logarithmic, exponential, and power models. It is important to note that the model should apply only within the scope of the provided data.

**Instructions:**
1. Use a calculator or computer software to generate a scatterplot for the given data.
2. Fit multiple models to the data and compare their effectiveness using the regression equations provided.
3. Evaluate the fit of each model by comparing the values of $ R^2 $.

**Data:**

| $ x $ | 1 | 4 | 5 | 9 | 11 | 16 |
|---------|----|----|----|----|----|----|
| $ y $ | 9 | 13 | 25 | 27 | 31 | 46 |

**Potential Regression Models:**

1. **Linear Model:**
\[
y = 7.04 + 2.36x
\]

2. **Exponential Model:**
\[
y = 8.14x^{0.58}
\]

3. **Logarithmic Model:**
\[
y = 4.40 + 12.02 \ln x
\]

4. **Quadratic Model:**
\[
y = 0.01x^2 - 2.19x + 7.53
\]

**Steps to Complete:**

1. **Scatterplot:**
- Plot the given data points $(x, y)$ on a graph.
- Observe the trend of the points to get a preliminary idea of which model might fit well.

2. **Model Fitting:**
- Fit the linear, exponential, logarithmic, and quadratic models to the data.
- Use software tools to obtain the regression equations and the $ R^2 $ values.

3. **Comparison:**
- Analyze which model provides the highest $ R^2 $ value, indicating the best fit.
- Confirm that the best-fit model logically aligns with the data's trend.

By successfully completing this exercise, students will gain experience in data analysis and model fitting,

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