Use the table to find the following, unit price being your (x) and units sold (y). a. Find linear correlation coefficient. Years of Experience Salary in 1000$ 15 3 28 42 13 64 50 16 90 11 58 1 9. 54 b. Find the line of best fit. c. How many units will sell if the unit price was 0.85.
Use the table to find the following, unit price being your (x) and units sold (y). a. Find linear correlation coefficient. Years of Experience Salary in 1000$ 15 3 28 42 13 64 50 16 90 11 58 1 9. 54 b. Find the line of best fit. c. How many units will sell if the unit price was 0.85.
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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
![**Question 3: Analyzing Data Using Linear Regression Techniques**
**a. Find Linear Correlation Coefficient.**
To start, we must calculate the linear correlation coefficient for the given data set. The data pairs are given in a table with the "Years of Experience" as the independent variable (x) and "Salary in 1000$" as the dependent variable (y).
| Years of Experience | Salary in 1000$ |
|---------------------|-----------------|
| 2 | 15 |
| 3 | 28 |
| 5 | 42 |
| 13 | 64 |
| 8 | 50 |
| 16 | 90 |
| 11 | 58 |
| 1 | 8 |
| 9 | 54 |
**b. Find the Line of Best Fit.**
The line of best fit is a straight line drawn through the center of a group of data points plotted on a scatter plot. This line represents the best estimate of the relationship between the variables. The linear equation is typically written as:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
**c. Predict Sales Based on Unit Price**
Using the line of best fit found in part (b), determine the expected number of units sold if the unit price was 0.85.
**Calculation Steps:**
1. Construct a scatter plot of the data points.
2. Use formulas for the linear regression line to calculate the slope (\( m \)) and y-intercept (\( b \)).
3. Substitute \( x = 0.85 \) into the regression equation to predict the corresponding \( y \)-value.
These steps can be performed using statistical software or a graphing calculator to expedite calculations. Observing the trend and assessing the strength of the relationship between variables can provide insight into the significance of the correlation and predictive power of the derived model.
**Educational Purpose:**
Through this exercise, students will learn to:
1. Calculate the linear correlation coefficient to measure the strength and direction of a linear relationship.
2. Determine the equation of the line of best fit to model data through linear regression.
3. Use regression equations for predictions, reinforcing the connection between algebraic and real-world applications.
Analyzing this dataset will also lend understanding to how empirical relationships are](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67f8d32e-7653-460d-a7f7-5cc77c157184%2F425bd360-a31e-4311-9b7a-d3c1ff050819%2Fw9jytdb.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 3: Analyzing Data Using Linear Regression Techniques**
**a. Find Linear Correlation Coefficient.**
To start, we must calculate the linear correlation coefficient for the given data set. The data pairs are given in a table with the "Years of Experience" as the independent variable (x) and "Salary in 1000$" as the dependent variable (y).
| Years of Experience | Salary in 1000$ |
|---------------------|-----------------|
| 2 | 15 |
| 3 | 28 |
| 5 | 42 |
| 13 | 64 |
| 8 | 50 |
| 16 | 90 |
| 11 | 58 |
| 1 | 8 |
| 9 | 54 |
**b. Find the Line of Best Fit.**
The line of best fit is a straight line drawn through the center of a group of data points plotted on a scatter plot. This line represents the best estimate of the relationship between the variables. The linear equation is typically written as:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
**c. Predict Sales Based on Unit Price**
Using the line of best fit found in part (b), determine the expected number of units sold if the unit price was 0.85.
**Calculation Steps:**
1. Construct a scatter plot of the data points.
2. Use formulas for the linear regression line to calculate the slope (\( m \)) and y-intercept (\( b \)).
3. Substitute \( x = 0.85 \) into the regression equation to predict the corresponding \( y \)-value.
These steps can be performed using statistical software or a graphing calculator to expedite calculations. Observing the trend and assessing the strength of the relationship between variables can provide insight into the significance of the correlation and predictive power of the derived model.
**Educational Purpose:**
Through this exercise, students will learn to:
1. Calculate the linear correlation coefficient to measure the strength and direction of a linear relationship.
2. Determine the equation of the line of best fit to model data through linear regression.
3. Use regression equations for predictions, reinforcing the connection between algebraic and real-world applications.
Analyzing this dataset will also lend understanding to how empirical relationships are
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