The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age in years (X1) and their gender (X2) (0 if male and 1 if female). The yearly income of a 24-year-old female individual is
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.
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age in years (X1) and their gender (X2) (0 if male and 1 if female).
The yearly income of a 24-year-old female individual is
![### Linear Regression Model
The equation displayed represents a linear regression model used for predictive analysis:
\[
\hat{y} = 30 + 0.7x_1 + 3x_2
\]
#### Explanation:
- **\(\hat{y}\)**: This is the predicted value of the dependent variable.
- **30**: This is the intercept term (also known as the constant term) of the model. It indicates the expected value of \(\hat{y}\) when \(x_1\) and \(x_2\) are both zero.
- **0.7**: This is the coefficient for \(x_1\), representing the change in \(\hat{y}\) for a one-unit change in \(x_1\), assuming \(x_2\) remains constant.
- **\(x_1\)**: This is the first independent variable in the model.
- **3**: This is the coefficient for \(x_2\), representing the change in \(\hat{y}\) for a one-unit change in \(x_2\), assuming \(x_1\) remains constant.
- **\(x_2\)**: This is the second independent variable in the model.
### Usage:
In practical applications, such a model can be used to predict outcomes based on the values of \(x_1\) and \(x_2\). For example, in an educational setting, \(x_1\) could represent hours of study per week, and \(x_2\) could represent attendance rate, while \(\hat{y}\) represents the predicted score on an exam.
By adjusting the values of \(x_1\) and \(x_2\), educators and students can estimate the impact of study and attendance on exam scores.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45c9d9ea-9d85-4e17-bbcb-fa0288237f89%2F4289693b-4728-4931-8889-d8a7292e8e9f%2Fhjdicws.png&w=3840&q=75)
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