Equation 8.1 Equation 18,5 TestScore; = Bo + BiIncome; + BIncome + uj, Y = Xß + U. Equation 18.20 RB = r,
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.
Consider the population regression of test scores against income and the
square of income in Equation (8.1).
a. Write the regression in Equation (8.1) in the matrix form of Equation
(18.5). Define Y, X, U, and β.
b. Explain how to test the null hypothesis that the relationship between
test scores and income is linear against the alternative that it is quadratic.
Write the null hypothesis in the form of Equation (18.20).
What are R, r, and q?
Find all Equations in attachment.
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