### Impact of Assembly Line Speed on Defective Parts in Manufacturing#### IntroductionIn a manufacturing process, the assembly line speed (measured in feet per minute) was hypothesized to influence the number of defective parts produced during the impaction process. To investigate this theory, managers set up an experiment where the same batch of parts was visually inspected at various line speeds. The following data was collected:#### Data Collected| Line Speed (x) | Number of Defective Parts Found (y) ||----------------|--------------------------------------|| 20 | 21 || 20 | 19 || 40 | 15 || 30 | 16 || 60 | 14 || 40 | 17 |#### Instructions- Use Microsoft Excel to generate the regression output for the given data.- Utilize the regression output to answer the subsequent questions provided.### Detailed Explanation1. **Line Speed (x)**: This column represents the speed of the assembly line in feet per minute.2. **Number of Defective Parts Found (y)**: This column shows the number of defective parts detected at the corresponding line speed.#### Next Steps1. **Data Analysis**: - Input the given data into Excel. - Use Excel's regression analysis tool to derive the relationship between line speed and the number of defective parts.2. **Interpretation**: - Analyze the regression output to understand how changes in line speed affect the number of defective parts. - Answer the questions based on your findings from the regression analysis.By investigating the results, manufacturers can make informed decisions to optimize assembly line speed and reduce the number of defective parts produced. **Title: Linear Regression Analysis Using Microsoft Excel****Introduction:**This exercise involves utilizing Microsoft Excel to generate regression output for a given dataset. The dataset includes observations of line speed (x) and the number of defective parts found (y). You will use this regression output to answer a series of questions.**Dataset:**| Line Speed (x) | Number of Defective Parts Found (y) ||----------------|------------------------------------|| 20 | 21 || 20 | 19 || 40 | 15 || 30 | 16 || 60 | 14 || 40 | 17 |**Instructions:**1. **Develop the Estimated Regression Equation:** Use Microsoft Excel to determine the relationship between the line speed and the number of defective parts found. This involves generating the regression equation that best fits the provided data.2. **Predict the Number of Defective Parts:** Use the regression equation to predict the number of defective parts found when the line speed is 45 feet per minute.3. **Calculate the Coefficient of Determination:** The coefficient of determination (R²) indicates how well the regression equation fits the data. Compute R² to evaluate the goodness of fit for your regression model.By following these steps, you will be able to derive meaningful insights from the dataset and understand the relationship between line speed and defective parts found.

a. In this case line speed (x) is the independent variable and number of defective parts found (y)…

20 21 20 19 40 15 30 16 60 14 40 17 Use Microsoft Excel to generate regression output for this problem and use the information in the output to answer the following questions. a. Develop the estimated regression equation that relates line speed to the number of defective parts found. b. What is the number of defective parts found when the line speed is 45 fe per minute? c. Compute the coefficient of determination. Did the estimated regression equation provide a good fit to the data? 84°F

20 21 20 19 40 15 30 16 60 14 40 17 Use Microsoft Excel to generate regression output for this problem and use the information in the output to answer the following questions. a. Develop the estimated regression equation that relates line speed to the number of defective parts found. b. What is the number of defective parts found when the line speed is 45 fe per minute? c. Compute the coefficient of determination. Did the estimated regression equation provide a good fit to the data? 84°F

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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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### Impact of Assembly Line Speed on Defective Parts in Manufacturing

#### Introduction
In a manufacturing process, the assembly line speed (measured in feet per minute) was hypothesized to influence the number of defective parts produced during the impaction process. To investigate this theory, managers set up an experiment where the same batch of parts was visually inspected at various line speeds. The following data was collected:

#### Data Collected

| Line Speed (x) | Number of Defective Parts Found (y) |
|----------------|--------------------------------------|
| 20 | 21 |
| 20 | 19 |
| 40 | 15 |
| 30 | 16 |
| 60 | 14 |
| 40 | 17 |

#### Instructions
- Use Microsoft Excel to generate the regression output for the given data.
- Utilize the regression output to answer the subsequent questions provided.

### Detailed Explanation
1. **Line Speed (x)**: This column represents the speed of the assembly line in feet per minute.
2. **Number of Defective Parts Found (y)**: This column shows the number of defective parts detected at the corresponding line speed.

#### Next Steps
1. **Data Analysis**:
- Input the given data into Excel.
- Use Excel's regression analysis tool to derive the relationship between line speed and the number of defective parts.

2. **Interpretation**:
- Analyze the regression output to understand how changes in line speed affect the number of defective parts.
- Answer the questions based on your findings from the regression analysis.

By investigating the results, manufacturers can make informed decisions to optimize assembly line speed and reduce the number of defective parts produced.

**Title: Linear Regression Analysis Using Microsoft Excel**

**Introduction:**
This exercise involves utilizing Microsoft Excel to generate regression output for a given dataset. The dataset includes observations of line speed (x) and the number of defective parts found (y). You will use this regression output to answer a series of questions.

**Dataset:**

| Line Speed (x) | Number of Defective Parts Found (y) |
|----------------|------------------------------------|
| 20 | 21 |
| 20 | 19 |
| 40 | 15 |
| 30 | 16 |
| 60 | 14 |
| 40 | 17 |

**Instructions:**

1. **Develop the Estimated Regression Equation:**
Use Microsoft Excel to determine the relationship between the line speed and the number of defective parts found. This involves generating the regression equation that best fits the provided data.

2. **Predict the Number of Defective Parts:**
Use the regression equation to predict the number of defective parts found when the line speed is 45 feet per minute.

3. **Calculate the Coefficient of Determination:**
The coefficient of determination (R²) indicates how well the regression equation fits the data. Compute R² to evaluate the goodness of fit for your regression model.

By following these steps, you will be able to derive meaningful insights from the dataset and understand the relationship between line speed and defective parts found.

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