Linear regression is a predicative analysis procedure that seeks to establish the relationship between two or more variables. The simplest form of a linear equation is Y= a + bX where; Y is the criterion (dependent) variable, “a” is a constant (intercept), b represents the slope of the line and X is the predictor (independent) variable. Plotting this graph yields a scatter plot that can indicate whether there exists a linear relationship between variables or not. If there is only one independent variable, then we use simple linear regression. Multiple linear regression applies to cases where there are two or more independent variables.

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## Application of Linear Regression

Linear regression has the following major applications;

- Establishing the strength of an independent variable
- Forecasting occurrences
- Forecasting trends

While it is useful in various fields like economics, business, statistics, biostatistics and others, linear regression has some shortcomings. These include;

- It assumes that the dependent and independent variables have a linear relationship
- Possibility of overfitting if observations are few
- Affected by outliers
- Affected by multi-collinearity, which must be removed before linear regression is applied.

## Improving Statistical Power of Linear Regression in Predicting Outcomes and/or Associations

A statistical power helps to establish if a certain effect truly exists. In regression analysis, the statistical power is a percentage/ probability indicating a correlation different from zero. To improve this statistical power, one has to vary the number of observations under study. Techniques such as Cohen’s f^{2} and the G*Power come in handy to calculate this power. If you need assistance with the same, we have the right professionals.

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