MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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  1. Use the table to find the following, unit price being your (x) and units sold (y).

    a) Find the linear correlation coefficient.
     
    b) Find the line of best fit.
  • c)How many units will sell if the unit price was 0.85.
### Statistical Analysis and Data Interpretation Problem

#### Problem Statement:
Given a table representing the relationship between years of experience and salary (in thousands of dollars), perform the following tasks:

1. **Find the linear correlation coefficient between years of experience and salary.**
2. **Determine the line of best fit for the given data.**
3. **Predict the number of units that will sell if the unit price is $0.85.**

#### Data Table:
The table below shows the years of experience and corresponding salaries (in $1000):

| Years of Experience | Salary in $1000 |
|---------------------|-----------------|
| 2                   | 15              |
| 3                   | 28              |
| 5                   | 42              |
| 13                  | 64              |
| 8                   | 50              |
| 16                  | 90              |
| 11                  | 58              |
| 1                   | 8               |
| 9                   | 54              |

### Task Breakdown:
**a. Find the linear correlation coefficient.**
   The linear correlation coefficient (also known as Pearson's correlation coefficient) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where:
   - 1 indicates a perfect positive linear relationship,
   - -1 indicates a perfect negative linear relationship,
   - 0 indicates no linear relationship.

**b. Find the line of best fit.**
   The line of best fit (or regression line) is a straight line that best represents the data points on a scatter plot. This line can be represented by the equation of a line, \( y = mx + b \), where:
   - \( y \) is the dependent variable (salary),
   - \( x \) is the independent variable (years of experience),
   - \( m \) is the slope of the line,
   - \( b \) is the y-intercept.

**c. Predict the number of units that will sell if the unit price is $0.85.**
   This involves using the line of best fit equation determined in part b. By inputting the unit price value into the equation, we can predict the corresponding number of units sold.

### Detailed Graph Explanation:
The table can be visualized in a scatter plot with:
   - **X-axis:** Years of experience
   - **Y-axis:** Salary in $1000
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Transcribed Image Text:### Statistical Analysis and Data Interpretation Problem #### Problem Statement: Given a table representing the relationship between years of experience and salary (in thousands of dollars), perform the following tasks: 1. **Find the linear correlation coefficient between years of experience and salary.** 2. **Determine the line of best fit for the given data.** 3. **Predict the number of units that will sell if the unit price is $0.85.** #### Data Table: The table below shows the years of experience and corresponding salaries (in $1000): | Years of Experience | Salary in $1000 | |---------------------|-----------------| | 2 | 15 | | 3 | 28 | | 5 | 42 | | 13 | 64 | | 8 | 50 | | 16 | 90 | | 11 | 58 | | 1 | 8 | | 9 | 54 | ### Task Breakdown: **a. Find the linear correlation coefficient.** The linear correlation coefficient (also known as Pearson's correlation coefficient) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where: - 1 indicates a perfect positive linear relationship, - -1 indicates a perfect negative linear relationship, - 0 indicates no linear relationship. **b. Find the line of best fit.** The line of best fit (or regression line) is a straight line that best represents the data points on a scatter plot. This line can be represented by the equation of a line, \( y = mx + b \), where: - \( y \) is the dependent variable (salary), - \( x \) is the independent variable (years of experience), - \( m \) is the slope of the line, - \( b \) is the y-intercept. **c. Predict the number of units that will sell if the unit price is $0.85.** This involves using the line of best fit equation determined in part b. By inputting the unit price value into the equation, we can predict the corresponding number of units sold. ### Detailed Graph Explanation: The table can be visualized in a scatter plot with: - **X-axis:** Years of experience - **Y-axis:** Salary in $1000
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