### Determining Linear Regression for an Unknown Metal Sample**Problem Statement:**An unknown metal has been discovered and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expresses mass as a function of the volume.**Experimental Data:**| Grams (g) | Volume (mL) ||-----------|-------------|| 20 | 386.4 || 21.5 | 407.1 || 23 | 444.4 || 24.5 | 463.9 || 26 | 492.3 || 27.5 | 536.6 || 29 | 565.9 |**Tasks:**A) **Determine the Linear Regression Equation:**Write the linear regression equation for the data in the chart. \[ \text{Volume} = \_\_\_ x + \_\_\_ \]where $ x $ is the grams of the unknown metal. Round your answers to 3 decimal places.B) **Predict Volume for a Given Mass:**If the mass of an unknown metal is 18 grams, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place.\[ \_\_\_ \text{ mL} \]#### Instructions for Part A:1. Calculate the slope (m) and y-intercept (b) of the best-fit line for the given data.2. Formulate the linear equation in the format: \[ \text{Volume} = mx + b \]#### Instructions for Part B:1. Substitute $ x = 18 $ grams into the unrounded regression equation.2. Solve for the Volume.3. Round the final predicted volume to one decimal place.**Note:** Ensure precise calculations by using statistical software or a calculator capable of performing linear regression analysis if available.

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An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expresses mass as a function of the volume. grams Volume in ml 20 386.4 21.5 407.1 23 444.4 24.5 463.9 26 492.3 27.5 536.6 29 565.9 A) Write the linear regression equation for the data in the chart. Volume = x + where x is the grams of the unknown metal. Round your answers to 3 decimal places B) If the mass of an unknown metal is 18, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place. mL

An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expresses mass as a function of the volume. grams Volume in ml 20 386.4 21.5 407.1 23 444.4 24.5 463.9 26 492.3 27.5 536.6 29 565.9 A) Write the linear regression equation for the data in the chart. Volume = x + where x is the grams of the unknown metal. Round your answers to 3 decimal places B) If the mass of an unknown metal is 18, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place. mL

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.

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### Determining Linear Regression for an Unknown Metal Sample

**Problem Statement:**
An unknown metal has been discovered and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expresses mass as a function of the volume.

**Experimental Data:**

| Grams (g) | Volume (mL) |
|-----------|-------------|
| 20 | 386.4 |
| 21.5 | 407.1 |
| 23 | 444.4 |
| 24.5 | 463.9 |
| 26 | 492.3 |
| 27.5 | 536.6 |
| 29 | 565.9 |

**Tasks:**

A) **Determine the Linear Regression Equation:**
Write the linear regression equation for the data in the chart.

\[ \text{Volume} = \_\_\_ x + \_\_\_ \]

where $ x $ is the grams of the unknown metal. Round your answers to 3 decimal places.

B) **Predict Volume for a Given Mass:**
If the mass of an unknown metal is 18 grams, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place.

\[ \_\_\_ \text{ mL} \]

#### Instructions for Part A:
1. Calculate the slope (m) and y-intercept (b) of the best-fit line for the given data.
2. Formulate the linear equation in the format: \[ \text{Volume} = mx + b \]

#### Instructions for Part B:
1. Substitute $ x = 18 $ grams into the unrounded regression equation.
2. Solve for the Volume.
3. Round the final predicted volume to one decimal place.

**Note:** Ensure precise calculations by using statistical software or a calculator capable of performing linear regression analysis if available.

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