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Line of Best Fit/ Least Squares Regression LIne - Essay Example

Extract of sample Line of Best Fit/ Least Squares Regression LIne

The term "regression", is mainly used to find the relationship between two or more variables used in different context. The method was first used to examine the relationship between the heights of fathers and sons. The two were related, and found that a tall father tended to have sons shorter than him; a short father tended to have sons taller than him. The height of sons regressed to the mean. The term linear regression is also referred to as the lines of regression.
is a linear equation with dependent variable y and independent variable x. When we draw a graph of this equation we obtain points which cluster in a particular direction which gives us the linear relationship between the two variables apart from the error or residual.
We have the y-value of the data set and we have the y-value given by the equation y = a x + b (remember a is slope, x is x-value, and b is y-intercept). In order to calculate the line of best fit we make use of the principle or method of least squares.In general the goal of linear regression is to find the line of best fit which gives or predicts the value of y from x or the value of x from y. It can be done by minimizing the sum of squares of the vertical distances of the points from the line. ...
Equation of the form y= a + b x
is a linear equation with dependent variable y and independent variable x. When we draw a graph of this equation we obtain points which cluster in a particular direction which gives us the linear relationship between the two variables apart from the error or residual.
We have the y-value of the data set and we have the y-value given by the equation y = a x + b (remember a is slope, x is x-value, and b is y-intercept). In order to calculate the line of best fit we make use of the principle or method of least squares.In general the goal of linear regression is to find the line of best fit which gives or predicts the value of y from x or the value of x from y. It can be done by minimizing the sum of squares of the vertical distances of the points from the line. It assumes that the data is linear and finds the slope and intercept that make a line which is straight and best fit for the data.
Multiple linear regression

In multiple linear regression models the variable is influenced by many factors. When we have a variable being compared to lot of factors or lots of comparisons are to be made .For example if the IQ quotient of the students of a class are to be compared we first find the most talented person of the class and then compare him with all the other students in order to test the IQ quotient of all the students. This can be done by least squares method.

The multiple linear regression equation is of the form
y=a1+a2x2+a3x3+a4x4+--------------------
We again solve this equation by the same method of least squares where multiple equations are to be solved to obtain the curve of best fit.

Summary

Many statistical quality control problems need the linear relationship between two or more variables. To find the linear relationship between two variables that is variable x and variable y we plot a graph taking the variables of x on the horizontal bar and the variables of y on the vertical bar .When we plot a graph we obtain the dots which tend to cluster along a well defined direction which suggests a linear relationship between the two variables x and y.
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