Suppose that we have collected the following predictor values and response values from four individuals from the same population: Individual i 1 2 3 4 Response 3 2 4 Predictor 6. 1 2 2 3 We want to use these four observations to find the estimated simple linear relationship of the form Yi = Bo + B1x¡ + e¡.
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.
Using this model, set up the system of equations representing the relationship between the predictor and response for these four individuals. Then using these, write expressions for each individual's residual and the residual sum of squares equation. Then find the corresponding score equations and solve for the least squares estimates of the slope and intercept.
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