Regression involves the concept of understanding the relationship between the dependent and independent variables. For example, take a case where you want to forecast sales of the business after realizing that their variation is affected by the GDP. In this case, the sales are the dependent variables which depend on the value of GDP. Regression analysis attempts to assess the strength and nature (covariance) of the relationship between the two variables.
Covariance
The covariance helps in determining the effect changes in an independent variable to dependent variable. The relationship (covariance) will be negative if one variable moves in the opposite directions (up and down).
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For a better interpretation and application of covariance in making sale forecast, it is important to calculate the correlation coefficient. It measures the range of variables variation between -1 and +1.
Correlation Coefficient
Similarly, the regression equation is the prime method of forecasting the desired variables. From the table below, a simple linear regression can be formulated (y=a +b x). Where “y” is the variable forecasted (dependent), “x” is the independent variable, “b” is the regression slope and “a” is the y-intercept which gives the value of a dependent variable when the independent variable is zero.
Year | Sales | GDP |
2014 | 100 | 1.00% |
2015 | 250 | 1.90% |
2016 | 275 | 2.40% |
2017 | 200 | 2.60% |
The line of the best fit of the linear regression will be as follows:
Regression Statistics
Regression Statistics | Coefficients | Intercept | 34.58409 |
Multiple R | 0.8292243 | GDP | 88.15552 |
R Square | 0.687613 | - | - |
Adjusted | - | - | |
R Square | - | - | |
In the statistical regression, the major outputs are the GDP coefficient, R-squared, and the intercept. In this case, for instance, R-squared provides the level of accuracy is making sale forecasts. The intercept provides the level of outputs when the GDP is zero and correlation coefficient provides the level of output when the GDP changes with 1%.
References
Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example . John Wiley & Sons.
Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation . Guilford Publications.
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2015). Introduction to linear regression analysis . John Wiley & Sons.
