The extended least squares assumptions are 1. E(u; X;) = 0 (u, has conditional mean zero); 2. (X;, Y;), i = 1, . .. , n, are independently and identically distributed (i.i.d.) draws from their joint distribution; 3. X; and u; have nonzero finite fourth moments; 4. X has full column rank (there is no perfect multicollinearity); 5. var(u;|X;) = oi (homoskedasticity); and 6. The conditional distribution of u; given X, is normal (normal errors). dependent variable and two regressors Sample Covariances Sample Means Y X, х, 6.39 0.26 0.22 0.32 7.24 0.80 0.28 х, 4.00 2.40
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.
Suppose that a sample of n = 20 households has the sample means and
sample
a. Calculate the OLS estimates of β0, β1, and β2. Calculate s2u. Calculate
the R2 of the regression.
b. Suppose that all six assumptions in Key Concept 18.1 hold. Test the
hypothesis that β1 = 0 at the 5% significance level.
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