Regression Analysis Of Carl Friedrich Gauss

History
Regression analysis is a statistical tool for investigating the relationship between variables. It is frequently used to predict the future and understand which factors cause an outcome.
The legendary German mathematician Carl Friedrich Gauss claimed his alleged discovery of statistical regression.
The method seemed so obvious to Gauss that he figured he must not have been the first to use it. He was sure enough it must have been discovered that he did not publicly state his finding until many years later, after his contemporary Adrien-Marie Legendre had published on the method. When Gauss suggested he had used it before Legendre it set off “one of the most famous priority disputes in the history of science...” Gauss would eventually

First, linear regression needs the relationship between the independent and dependent variables to be linear. It is also important to check for outliers since linear regression is sensitive to outlier effects. The linearity assumption can best be tested with scatter plots, the following two examples depict two cases, where no and little linearity is present.

2. Secondly, the linear regression analysis requires all variables to be multivariate normal. This assumption can best be checked with a histogram or a Q-Q-Plot. Normality can be checked with a goodness of fit test, e.g., the Kolmogorov-Smirnov test. When the data is not normally distributed a non-linear transformation (e.g., log-transformation) might fix this issue.

3. Thirdly, linear regression assumes that there is little or no multicollinearity in the data. Multicollinearity occurs when the independent variables are too highly correlated with each other.

4. Fourth, linear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other. For instance, this typically occurs in stock prices, where the price is not independent from the previous price.