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Q: Why Simple linear regression is important?

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No.

+ Linear regression is a simple statistical process and so is easy to carry out. + Some non-linear relationships can be converted to linear relationships using simple transformations. - The error structure may not be suitable for regression (independent, identically distributed). - The regression model used may not be appropriate or an important variable may have been omitted. - The residual error may be too large.

To see if there is a linear relationship between the dependent and independent variables. The relationship may not be linear but of a higher degree polynomial, exponential, logarithmic etc. In that case the variable(s) may need to be transformed before carrying out a regression. It is also important to check that the data are homoscedastic, that is to say, the error (variance) remains the same across the values that the independent variable takes. If not, a transformation may be appropriate before starting a simple linear regression.

Regression :The average Linear or Non linear relationship between Variables.

on the lineGiven a linear regression equation of = 20 - 1.5x, where will the point (3, 15) fall with respect to the regression line?Below the line

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I want to develop a regression model for predicting YardsAllowed as a function of Takeaways, and I need to explain the statistical signifance of the model.

No.

+ Linear regression is a simple statistical process and so is easy to carry out. + Some non-linear relationships can be converted to linear relationships using simple transformations. - The error structure may not be suitable for regression (independent, identically distributed). - The regression model used may not be appropriate or an important variable may have been omitted. - The residual error may be too large.

To see if there is a linear relationship between the dependent and independent variables. The relationship may not be linear but of a higher degree polynomial, exponential, logarithmic etc. In that case the variable(s) may need to be transformed before carrying out a regression. It is also important to check that the data are homoscedastic, that is to say, the error (variance) remains the same across the values that the independent variable takes. If not, a transformation may be appropriate before starting a simple linear regression.

One of the main reasons for doing so is to check that the assumptions of the errors being independent and identically distributed is true. If that is not the case then the simple linear regression is not an appropriate model.

Regression :The average Linear or Non linear relationship between Variables.

Linear regression can be used in statistics in order to create a model out a dependable scalar value and an explanatory variable. Linear regression has applications in finance, economics and environmental science.

Simple linear regression is performed between one independent variable and one dependent variable. Multiple regression is performed between more than one independent variable and one dependent variable. Multiple regression returns results for the combined influence of all IVs on the DV as well as the individual influence of each IV while controlling for the other IVs. It is therefore a far more accurate test than running separate simple regressions for each IV. Multiple regression should not be confused with multivariate regression, which is a much more complex procedure involving more than one DV.

Simple regression is used when there is one independent variable. With more independent variables, multiple regression is required.

Linear Regression is a method to generate a "Line of Best fit" yes you can use it, but it depends on the data as to accuracy, standard deviation, etc. there are other types of regression like polynomial regression.

on the lineGiven a linear regression equation of = 20 - 1.5x, where will the point (3, 15) fall with respect to the regression line?Below the line

You use it when the relationship between the two variables of interest is linear. That is, if a constant change in one variable is expected to be accompanied by a constant [possibly different from the first variable] change in the other variable. Note that I used the phrase "accompanied by" rather than "caused by" or "results in". There is no need for a causal relationship between the variables. A simple linear regression may also be used after the original data have been transformed in such a way that the relationship between the transformed variables is linear.