STATISTICS II (İSTATİSTİK II) - (İNGİLİZCE) Dersi Correlation and Regression Analysis soru detayı:

PAYLAŞ:

SORU:

Explain simple linear regression. 


CEVAP:

here, there will be only one independent variable and one dependent variable, it is called simple linear regression analysis.
Let’s say that, in a data set there are observed values of two variables, with n observations, x = x1, x2, x3,..., xn and y = y1, y2, y3, ..., yn. In order to show a possible linear relationship between independent variable (x) and dependent variable (y), the following simple linear regression model can be written;
yi =? +ßxi +?i
In this simple linear regression model:
yi: i th observation’s value of the dependent variable,
xi: i th observation’s value of the independent variable,
?i : random error (the mean of it is zero),
? and ß : the population parameters to be estimated by sample data.


In simple linear regression, a model is created by using the sample data. As it may be seen from the equation for regression model given above, the value of the dependent variable is divided into some components. In the model, the random error ? represents the amount of variability in the dependent variable that cannot be explained by the linear relationship between independent and dependent variables. The regression model creates a line passing through the middle of data pairs and the method of least squares minimizes the overall distance of each data pair from the regression line. ? parameter is the intercept of the
regression line and ß is the slope of the regression line. ? parameter is usually called as the constant of the model.