Linear Regression Equation
SIMPLE LINEAR REGRESSION ANALYSIS
Regression Analysis is a simple statistical tool used to model the dependence of a
variable on one or more explanatory variables. It is the method used to describe the
nature of the relationship between variables, that is, either positive or negative, linear, or
nonlinear. This functional relationship may then be formally stated as an equation, with
associated statistical values that describe how well this equation fits the data.
Simple linear regression is the least estimator of a linear regression model with a
single predictor. The least-square model determines a regression equation by
minimizing the sum of squares of the vertical distances between the actual y values and
the predicted values of y meaning, simple linear regression fits a straight line through the
set of n points in such a way that makes the sum of squared residuals of the model as small as
possible. This method gives what is generally known as the "best-fitting" line.
The difference between an observed value and the predicted value is called
the residual. The mean of the residual is always zero.
The points that fall outside the overall pattern of the other points are known as outliers.
In a scatterplot, there are scores whose removal greatly changes the regression line
which is called influential scores. In some cases, these scores are restricted to points
with extreme x - values. Some influential scores may have a small residual but still,
have a greater effect on the regression line than scores with possibly larger residuals
but average x - values.
The following are the formula that we will use for Regression Analysis;
, Example:
The owner of a chain of fruit shake stores would like to find the correlation between
atmospheric temperature and sales during the summer season. A random sample of 12
days is selected with the results given as follows:
Determine the regression equation, then plot the regression line.
Solution:
SIMPLE LINEAR REGRESSION ANALYSIS
Regression Analysis is a simple statistical tool used to model the dependence of a
variable on one or more explanatory variables. It is the method used to describe the
nature of the relationship between variables, that is, either positive or negative, linear, or
nonlinear. This functional relationship may then be formally stated as an equation, with
associated statistical values that describe how well this equation fits the data.
Simple linear regression is the least estimator of a linear regression model with a
single predictor. The least-square model determines a regression equation by
minimizing the sum of squares of the vertical distances between the actual y values and
the predicted values of y meaning, simple linear regression fits a straight line through the
set of n points in such a way that makes the sum of squared residuals of the model as small as
possible. This method gives what is generally known as the "best-fitting" line.
The difference between an observed value and the predicted value is called
the residual. The mean of the residual is always zero.
The points that fall outside the overall pattern of the other points are known as outliers.
In a scatterplot, there are scores whose removal greatly changes the regression line
which is called influential scores. In some cases, these scores are restricted to points
with extreme x - values. Some influential scores may have a small residual but still,
have a greater effect on the regression line than scores with possibly larger residuals
but average x - values.
The following are the formula that we will use for Regression Analysis;
, Example:
The owner of a chain of fruit shake stores would like to find the correlation between
atmospheric temperature and sales during the summer season. A random sample of 12
days is selected with the results given as follows:
Determine the regression equation, then plot the regression line.
Solution:
