c. What is the number 0.286 called? O Regression coefficient O Coefficient of determination O Homoscedasticity O Multicollinearity d. As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.) The estimated performane increases by e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl's performance on the new machine. (Round your answer to 3 decimal places.) Estimated performane
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.
![c. What is the number 0.286 called?
- Regression coefficient
- Coefficient of determination
- Homoscedasticity
- Multicollinearity
d. As age increases by one year, how much does estimated performance on the new machine increase? **(Round your answer to 3 decimal places.)**
The estimated performance increases by [___] .
e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine. **(Round your answer to 3 decimal places.)**
Estimated performance [___]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1d17f5d-0c9d-4d20-b4d8-205cdade0cbf%2Fc4d2d379-af0f-441d-a6c4-8127730c0f66%2Fn3udqoe_processed.png&w=3840&q=75)
![**Title: Analyzing Performance on New Processing Machines**
**Introduction:**
Thompson Photo Works purchased new, sophisticated processing machines. The production department needed guidance on the qualifications needed by an operator. Key factors such as age and length of service might be relevant. To explore the factors affecting performance on new machines, four variables were considered:
- \( x_1 \): Length of time an employee was in the industry
- \( x_2 \): Mechanical aptitude test score
- \( x_3 \): Prior on-the-job rating
- \( x_4 \): Age
Performance on the new machine is designated \( y \).
**Data Collection:**
Thirty employees were selected randomly, and their performance data was recorded. A sample of this data is shown below:
| Name | Performance on New Machine, \( y \) | Length of Time in Industry, \( x_1 \) | Mechanical Aptitude Score, \( x_2 \) | Prior On-the-Job Performance, \( x_3 \) | Age, \( x_4 \) |
|---------------|-------------------------------------|--------------------------------------|--------------------------------------|-----------------------------------------|-----------------|
| Mike Miraglia | 112 | 12 | 312 | 121 | 52 |
| Sue Trythall | 113 | 2 | 380 | 123 | 27 |
**Equation Analysis:**
The following equation was used to estimate performance:
\[
\hat{y} = 11.6 + 0.4x_1 + 0.286x_2 + 0.112x_3 + 0.002x_4
\]
**Questions:**
**a. What is this equation called?**
- [ ] Multiple regression equation
- [ ] Multiple standard error of estimate
- [ ] Coefficient of determination
**b. How many dependent and independent variables are there?**
- **Dependent:** 1
- **Independent:** 4
**Discussion:**
This equation represents a multiple regression, where performance on the new machine (\( \hat{y} \)) is predicted based on four independent variables. Understanding the impact of each variable is crucial for optimizing operator selection and training.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1d17f5d-0c9d-4d20-b4d8-205cdade0cbf%2Fc4d2d379-af0f-441d-a6c4-8127730c0f66%2Fef4a8an_processed.png&w=3840&q=75)
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