REGRESSION ESTIMATOR USING STRATIFIED RANDOM SAMPLING

 Utkarsh Chaudhary

2048110

INTRODUCTION:

The ratio method of estimation uses the auxiliary information which is correlated with the study variable to improve the precision which results in the improved estimators when the regression of Y on X is linear and passes through the origin. When the regression of Y on X is linear, it is not necessary that the line should always pass through the origin. Under such conditions, it is more appropriate to use the regression type estimator to estimate the population means. 

Analogous to the ratio and product estimators, the linear regression estimator is also designed to increase the efficiency of estimation by using information on the auxiliary variable x which is correlated with the study variable y.

 

IMPORTANCE OF REGRESSION ESTIMATORS:

The importance of regression analysis is that it is all about data: data means numbers and figures that actually define your business. The advantages of regression analysis is that it can allow you to essentially crunch the numbers to help you make better decisions for your business currently and into the future. The importance of regression analysis for a small business is that it helps determine which factors matter most, which it can ignore, and how those factors interact with each other. The importance of regression analysis lies in the fact that it provides a powerful statistical method that allows a business to examine the relationship between two or more variables of interest.

 

FORMULAE FOR REGRESSION ESTIMATORS:



PROCEDURE OF USING REGRESSION ESTIMATOR USING STRATIFIED RANDOM SAMPLING:

First by using samplingbook we sort the data through different stratum sizes which can be according to any variable such as number, mean , standard deviation etc. Then by using as.vector we can estimate the stratified random sample and start working on finding our regression estimator.

Through the libraries SDaA and survey we can begin our computations. Then by using summary function and using the values got from it we can obtain the regression estimates . We can also find out by comparing about which estimator is efficient if its regression or ratio.

 

R computations:

Suppose we have a dataset of a hospital and we wish to know the relationship between Body mass index and age of some specific patients who do not have diabetes then we can use regression estimators such that





Thus this example uses combination of Regression estimators and Stratified random sampling and we can find relationship between any variables using different stratums.

 

APPLICATION OF REGRESSION ESTIMATORS:

1.Predictive Analytics: 

Forecasting future opportunities and risks is the most prominent application of regression analysis in business. Demand analysis, for instance, predicts the number of items which a consumer will probably purchase.


2. Operation Efficiency:


Regression models can also be used to optimize business processes. A factory manager, for example, can create a statistical model to understand the impact of oven temperature on the shelf life of the cookies baked in those ovens

 

3. Correcting Errors:


Regression is not only great for lending empirical support to management decisions but also for identifying errors in judgment. For example, a retail store manager may believe that extending shopping hours will greatly increase sales.




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