What is a simple linear regression?

Simple linear regression applies to statistics and helps describe (x, y) data that seems to have a linear relationship, allowing a certain forecast to be known if it is known. These data are often rendered on the scattering and the formula for linear regression creates a line that best suits all points if they actually have linear correlation. Not all points are closed, but it should be a line where the sum of the squares of the difference between the actual data and the expected data (residues) creates the lowest number, often called the line of the smallest squares or line. The line equation for samples and population data are as follows: ŷ = b _{0 + b 1 x and y = b 0 + b x.}

Anyone who is familiar with algebroue or m. The reason for this regrouping is that it is then elegantly easy to add other terms with functions such as exponents that could describe different non -linear forms of relationship.

The formula for obtaining a simple linear regression line is relatively complex and cumbersome, and most people do not spend much time writing because it takes a long time. Instead, various programs, such as Excel® or for many types of scientific calculators, can easily calculate the line of the smallest squares. The line is only suitable for prediction if there is clear evidence of a strong correlation between data sets (x, y). The calculator generates the line, regardless of whether it makes sense to use it.

At the same time, a simple equation of linear regression line is generated, people have to look at the level of correlation. This means the R, the correlaficient of the ator, against the table of values ​​to determine whether there is a linear correlation. In addition, data evaluation by bringing as a scattering is a good way to get meaning if the data have a linear relationship.

What can then be done using a simple linear regression line, if it has linear correlation, is that LZ valuesE to replace the X to obtain the predicted value for ŷ. This forecast has its limits. The present data, especially if it is only a sample, may now have linear correlation, but may not later with the addition of additional sampling material.

alternately, the whole sample can share correlation while the whole population is not. The prediction is therefore limited and exceeding the available data values ​​is called extrapolation and is not supported. In addition, if people knew that if there is no linear correlation, the best estimated x is the diameter of all data y.

essentially, the simple linear regression is a useful statistical tool that can be used with discretion to predict ŷ X -based values. It almost always learns the idea of ​​linear correlation, as the determination of the usefulness of the regression line requires an analysis of r. Fortunately, with many modern technical programs, people can graph distractions, add regression line and determine the correlation coefficient R with several records.