Consider the differences between a linear trend forecast a s

Consider the differences between a linear trend forecast, a simple linear regression, and a multiple linear regression. What are some of the restrictions of each of the different forecasting techniques? Are there any circumstances when one technique would be preferred to the others?

Solution

There is much difference between the three techniques. I am highlighting the major ones.

1) Linear trend forecast is generally used to predict the time-series values. With some data from the previous time period T, we can make a time series model with some trend line. These type of data are self dependent. That means the dependent variable regresses itself to predict the future forecast. Like the weather forecast of one day relies on the weather of previous days. Although concepts of linear regression are used to build the linear trend forecast, its not generally used only for time dependent variables.

2) Simple linear regression is the linear equation representing the best fit possible between a dependent variable and an independent variable. Remember that there is only one independent variable in simple linear regression model. The simple linear regression model is the best method to forecast the values if there is some kind of linear relation between dependent and the independent variable. Its priniple is minimizing the sum of squares of errors. So, it is assumed to be the best possible method. The limitation of simple linear regression is that it can\'t be used for the case when there are more than one independent/predictor variables.

3) A multiple linear regression model is the extended version of simple linear regression. We use this predictive model when we have more than one independent/predictor variable. This is also based on the principle of minimizing the sum of squares. The concept of multiple linear regression are used in various time-series forecasting as well. But in that case the independent and dependent variable are correlated. While in case of multiple linear regression, the independent variable must not be correlated.

So, we can conclude that -

1) Linear trend forecast is used preferably when we have a time dependent data.

2) Simple linear regression is used when we have only one dependent and one independent variable.

3) Multiple linear regression is used when there are more than one independent variables.