alculate the ordinary least squares (OLS) estimates of the coefficients
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.
- A researcher wishes to investigate the association between two variables, denoted xi and yi. The following results have been obtained from the analysis of a sample of 30 observations:
Sxi = 119.2, Syi = 129.2, Sxi yi = 480.9, xSi2 = 493.6
(xi −x)2 = 20.4, ei2 =444.2
- Calculate the ordinary least squares (OLS) estimates of the coefficients of the linear regression, yi = β1 + β2xi +ui.
- What does your estimate of β2 in part (i) suggest about the association between xi and yi.
- Calculate the standard error of the regression, ˆ , and the standard error of the estimated slope coefficient, se(ˆ2) .
- Test the null hypothesis H0: 2=0 against the alternative hypothesis H1: 20, using a significance level of 0.05.
- On the basis of your hypothesis test in part (iv), is there any evidence of an association between xi and yi?
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