Suppose the population regression model, which shows the relationship between the explanatory variables (x1 and x2) and the dependent variable y, is given by log(y) = bo+! X1+b2x2+u Suppose the model has been estimated, and the results are as follows: log(y) = 5.1+2.6×1+0.9x2 Fill in the blanks below with the amount of rise in y and ŷ (y_hat) driven by causes provided in each sentence, respectively. From the coefficient estimate of b2, holding x1 constant, when x2 increases by 1 unit, y rises by %, which is an approximation that becomes more inaccurate as the change in log(y) increases. However, when x2 increases by one unit, y_hat rises by exactly %. When x2 decreases by one unit, y_hat falls by exactly %.
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.
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