2. Let kids denote the number of children ever born to a woman, and let educ denotes years of education of the woman. A simple regression model relating fertility to years of education is kids = Bo +B1educ + u, where u is the unobserved error. (1) What factors are contained in u (Please specify TWO factors)? How are these correlated with level of education? (2) Could you demonstrate, using ONE factor you answered in (1) as an example, that due to its correlation to education, the effect of education on number of kids born to a woman will be biasedly estimated. In particular, given the assumption you make on the correlation between that factor and educ as well as kids, will the coefficient of educ be overestimated or underestimated if directly using the regression model shown? (3) Again, using the factor you utilized in (2), show that what you could do in order to obtain an unbiased estimate of B1?

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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.