The following table maps unit sale values to the size in square feet. Using that data and the calculated regression line Value = $28,278+$37.144×SquareFeet,determine the errors associated with each observation and then construct a frequency distribution and histog
The following table maps unit sale values to the size in square feet. Using that data and the calculated regression line Value = $28,278+$37.144×SquareFeet,determine the errors associated with each observation and then construct a frequency distribution and histog
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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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
The following table maps unit sale values to the size in square feet. Using that data and the calculated regression line Value = $28,278+$37.144×SquareFeet,determine the errors associated with each observation and then construct a frequency distribution and histogram.
| Square Feet | Market Value |
| 1810 | 90300 |
| 1915 | 104400 |
| 1840 | 93200 |
| 1810 | 90900 |
| 1837 | 101800 |
| 2029 | 108600 |
| 1734 | 87500 |
| 1852 | 96100 |
| 1789 | 89200 |
| 1664 | 88500 |
| 1853 | 100900 |
| 1619 | 96800 |
| 1690 | 87400 |
| 2372 | 114000 |
| 2371 | 113300 |
| 1665 | 87600 |
| 2124 | 116100 |
| 1619 | 94800 |
| 1731 | 86300 |
| 1665 | 87200 |
| 1521 | 83300 |
| 1485 | 79800 |
| 1587 | 81500 |
| 1598 | 87000 |
| 1485 | 82600 |
| 1484 | 78900 |
| 1518 | 87500 |
| 1702 | 94300 |
| 1484 | 82100 |
| 1468 | 88000 |
| 1521 | 88000 |
| 1521 | 88600 |
| 1483 | 76700 |
| 1520 | 84400 |
| 1668 | 91000 |
| 1589 | 80900 |
| 1784 | 91400 |
| 1484 | 81300 |
| 1518 | 100700 |
| 1520 | 87300 |
| 1682 | 96800 |
| 1582 | 85100 |
Transcribed Image Text:### Histograms in Data Analysis
In this section, we will explore the concept of histograms and their application in analyzing data distributions. A histogram is a graphical representation of data that uses bars of varying heights to show the frequency of data points in successive numerical intervals.
#### Description of Histograms
Below are four histograms, each depicting the frequency distribution of "Error" in thousands. The x-axis represents the range of errors, measured in thousands, while the y-axis represents the frequency of data points within each range.
#### Details of the Histograms
- **Histogram a**:
- Range: -15 to 20 (thousands)
- Highest Frequency: Approximately 25, occurring at errors close to -5 (thousands)
- Distribution: Positively skewed with most data concentrated around -5 and tapering off towards the higher error values.
- **Histogram b**:
- Range: -15 to 20 (thousands)
- Highest Frequency: Approximately 20, occurring at errors between -5 and 5 (thousands)
- Distribution: Positively skewed with a higher frequency around the error value of 0 and less frequent higher error values.
- **Histogram c**:
- Range: -15 to 20 (thousands)
- Highest Frequency: Approximately 25, occurring at errors close to 0 (thousands)
- Distribution: Combines both left and right tails, with a concentration of frequency around the error value of 0 tapering off both at negative and positive extremes.
- **Histogram d**:
- Range: -15 to 20 (thousands)
- Highest Frequency: Approximately 25, occurring at errors close to -5 (thousands)
- Distribution: Shows a similar pattern to Histogram b, but with a noticeable drop-off after errors exceed 10.
#### Understanding the Graphs
These histograms are useful for:
1. **Identifying Patterns**: Understanding where the majority of data points lie.
2. **Detecting Outliers**: Observing any unusual deviations from the general pattern.
3. **Analyzing Skewness**: Recognizing whether the data is skewed towards a particular direction (positive or negative).
#### Practical Applications
Histograms are particularly useful in fields such as:
- **Quality Control**: To monitor process behavior over time.
- **Econometrics**: To analyze financial data distributions.
- **Healthcare**:
![### How to Construct a Frequency Distribution
A frequency distribution is a summary chart showing how frequently each of various outcomes in a set of data occurs. It is a useful tool for quickly identifying patterns in the data. Below, we present a template for constructing a frequency distribution. Follow the outlined steps to fill in the distribution yourself.
#### Step-by-Step Example
Consider the following data regarding the errors in a certain process. To create a frequency distribution, we need to count how many times the errors fall within each specified range.
#### Error Ranges and Corresponding Frequencies
| Error Range | Frequency |
|---------------------------|-----------|
| \(-15,000 < e_i \leq -10,000\) | [ ] |
| \(-10,000 < e_i \leq -5,000\) | [ ] |
| \(-5,000 < e_i \leq 0\) | [ ] |
| \(0 < e_i \leq 5,000\) | [ ] |
| \(5,000 < e_i \leq 10,000\) | [ ] |
| \(10,000 < e_i \leq 15,000\) | [ ] |
| \(15,000 < e_i \leq 20,000\) | [ ] |
Follow these steps to complete the table:
1. **Collect Data:** Gather all error measurements from your data set.
2. **Sort Data by Range:** Categorize each error into the appropriate range.
3. **Count Frequencies:** Count the number of errors falling into each range.
4. **Fill in Frequencies:** Enter these counts in the "Frequency" column of the table.
#### Example Data Set (for practice):
Suppose you have the following errors from your data set:
\[
-12,500, -8,000, -3,200, 1,400, 7,300, 12,800, 18,400 \]
Using this data set, fill in the "Frequency" column:
1. \(-15,000 < e_i \leq -10,000\): 1 (error: -12,500)
2. \(-10,000 < e_i \leq -5,000\): 1 (error: -8,000)
3. \(-5,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F276776e2-a533-44e1-9ab5-5479c168bd72%2Fab5bd67b-e6a5-45a1-bf9e-7bbbb0e02c4e%2F1wwu8h_processed.png&w=3840&q=75)
Transcribed Image Text:### How to Construct a Frequency Distribution
A frequency distribution is a summary chart showing how frequently each of various outcomes in a set of data occurs. It is a useful tool for quickly identifying patterns in the data. Below, we present a template for constructing a frequency distribution. Follow the outlined steps to fill in the distribution yourself.
#### Step-by-Step Example
Consider the following data regarding the errors in a certain process. To create a frequency distribution, we need to count how many times the errors fall within each specified range.
#### Error Ranges and Corresponding Frequencies
| Error Range | Frequency |
|---------------------------|-----------|
| \(-15,000 < e_i \leq -10,000\) | [ ] |
| \(-10,000 < e_i \leq -5,000\) | [ ] |
| \(-5,000 < e_i \leq 0\) | [ ] |
| \(0 < e_i \leq 5,000\) | [ ] |
| \(5,000 < e_i \leq 10,000\) | [ ] |
| \(10,000 < e_i \leq 15,000\) | [ ] |
| \(15,000 < e_i \leq 20,000\) | [ ] |
Follow these steps to complete the table:
1. **Collect Data:** Gather all error measurements from your data set.
2. **Sort Data by Range:** Categorize each error into the appropriate range.
3. **Count Frequencies:** Count the number of errors falling into each range.
4. **Fill in Frequencies:** Enter these counts in the "Frequency" column of the table.
#### Example Data Set (for practice):
Suppose you have the following errors from your data set:
\[
-12,500, -8,000, -3,200, 1,400, 7,300, 12,800, 18,400 \]
Using this data set, fill in the "Frequency" column:
1. \(-15,000 < e_i \leq -10,000\): 1 (error: -12,500)
2. \(-10,000 < e_i \leq -5,000\): 1 (error: -8,000)
3. \(-5,
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