For a particular value of a predictor variable, is there a difference between the predicted value of the response variable and the point estimate for the conditional mean of the response variable? Explain your answer.
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.
For a particular value of a predictor variable, is there a difference between the predicted value of the response variable and the point estimate for the conditional mean of the response variable? Explain your answer.
Introduction:
Suppose the population regression equation for a simple linear regression model of the response variable, y, on the predictor variable, x is:
y = β0 + β1 x + ε;
Here, β0 is the intercept β1 is the slope, and ε is the random error term.
Since the population regression model is hardly ever known, sample data is used to estimate the regression model. The sample regression model is:
ŷ = b0 + b1 x;
Here, b0 is the intercept and the point estimate of β0, b1 is the slope and the point estimate of β1, and ŷ is the predicted value of the response variable, y.
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