Question

TRUE/FALSE and explain Although applied regression analysis deals with the dependence of one variable on other variables, the results do not necessarily imply causation.

Answer 1

Answer : True

Explanation :

In statistics, regression analysis is a statistical technique for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables, called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.

Regression analysis is widely used for prediction and forecasting. Regression analysis is also used to understand which among the independent variables is related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable; for example, correlation does not imply causation.

• Regression models predict a value of the YY variable, given known values of the XX variables. Prediction within the range of values in the data set used for model-fitting is known informally as interpolation.
• Prediction outside this range of the data is known as extrapolation. The further the extrapolation goes outside the data, the more room there is for the model to fail due to differences between the assumptions and the sample data or the true values.
• There are certain necessary conditions for regression inference: observations must be independent, the mean response has a straight-line relationship with xx, the standard deviation of yy is the same for all values of xx, and the response yy varies according to a normal distribution.