Suppose you want to evaluate the effectiveness of a job training program using twage - Bo + Bprogram +u as a model. You take 1,000 employees and estimate the simple regression as:
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.
![### 15. Treatment effects without randomization
Suppose you want to evaluate the effectiveness of a job training program using \( \text{wage} = \beta_0 + \beta_1 \text{program} + u \) as a model. You take 1,000 employees and estimate the simple regression as:
\[ \widehat{\text{wage}} = 22.6 - 8.6 \text{program} \]
where:
- \( \text{wage} \) = hourly wage in dollars
- \( \text{program} \) = 1 if the employee participated in the training course, 0 otherwise
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Suppose that in addition to performing the simple regression, you perform a multiple regression with three controls that gives the following result:
\[ \widehat{\text{wage}} = 19.5 + 7.5 \text{program} + 0.9 \text{prewearn} + 0.8 \text{educ} - 0.65 \text{age} \]
where:
- \( \text{wage} \) = hourly wage in dollars
- \( \text{program} \) = 1 if the employee participated in the training course, 0 otherwise
- \( \text{prewearn} \) = hourly wage in dollars prior to the training course becoming available
- \( \text{educ} \) = years of education
- \( \text{age} \) = age in years
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The difference between \( \widehat{\text{wage}} \) and \( \widehat{\text{wage}} \) of an employee who participated in the training program is $ __________ per hour. (Hint: Calculate \( \widehat{\text{wage}} - \widehat{\text{wage}} \) holding \( \text{prewearn} \), \( \text{educ} \), and \( \text{age} \) constant when computing \( \widehat{\text{wage}} \).)
The difference between \( \widehat{\text{wage}} \) and \( \widehat{\text{wage}} \) of an employee who did not participate in the training program is $ __________ per hour. (Hint: Calculate \( \widehat{\text{wage}} - \widehat{\text{wage](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd920f800-7cb4-4708-a86f-fdc64006663e%2F0047b4da-7fdf-4fb0-8082-d4d8b8aafbb5%2Fbcvt4ys_processed.png&w=3840&q=75)
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