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 express mass as a function of the volume. Round your answers to 3 decimal places grams Volume in ml 19 51 20.5 55.6 22 60.9 23.5 63.1 25 67.8 26.5 71.9 28 76.7 Volume x + where x is the grams of the unknown metal ||
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.
![**Title: Linear Modeling of an Unknown Metal's Mass and Volume**
**Introduction:**
An unknown metal has been discovered, and the experimental results are summarized in the table below. The table contains the mass in grams of the metal and the corresponding volume in milliliters measured by water displacement. The task is to determine a linear model that expresses mass as a function of volume.
**Data Table:**
| Grams (g) | Volume (mL) |
|-----------|-------------|
| 19 | 51 |
| 20.5 | 55.6 |
| 22 | 60.9 |
| 23.5 | 63.1 |
| 25 | 67.8 |
| 26.5 | 71.9 |
| 28 | 76.7 |
**Objective:**
Find a linear model in the form \( \text{Volume} = mx + b \), where \( x \) represents the grams of the unknown metal. Round your answers to three decimal places.
**Additional Information:**
Below the table, there is an equation template:
\[ \text{Volume} = \_\_\_\_x + \_\_\_\_ \]
Use the data provided to calculate the values of \( m \) and \( b \) so that the volume can be predicted based on the mass of the unknown metal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c270b28-6c5f-463d-8853-d4f8b0737286%2F15918b5e-77cc-405c-b70d-20d1cda06faf%2F9vxfarj_processed.png&w=3840&q=75)
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