REGRESSION ESTIMATOR FOR SIMPLE RANDOM SAMPLING

 

      REGRESSION ESTIMATOR OF SIMPLE RANDOM SAMPLING

                                           ANNA THOMAS

                                             30/11/2020

 

INTRODUCTION:

Like ratio estimators, linear regression estimators also make use of auxiliary information for increasing precision. It was seen that the ratio estimator provides a precise estimate of the population mean if regression is linear and the line passes through the origin. When regression is linear and the line does not go through the origin, it is better to use estimators based on linear regression. In other words, if the study variate (y) is approximately a constant and a multiple of the auxiliary variate, it is more precise to estimate the population mean or total by fitting a linear regression. Such an estimator is called a regression estimator. Like the ratio estimator, the regression estimator is not unbiased for the population mean or total.

Regression estimator is the appropriate estimator for such situations. Although this estimator requires little more calculations than the ratio estimator, it is always at least as efficient as the ratio estimator for estimating the population mean or total. Similarly, the product estimator of population means or total is never more efficient than the corresponding linear regression estimator.

 

FORMULAE FOR REGRESSION ESTIMATOR




APPLICATION OF REGRESSION ESTIMATOR

1.    Linear regressions can be used in business to evaluate trends and make estimates or forecasts. For example, if a company’s sales have increased steadily every month for the past few years, by conducting a linear analysis on the sales data with monthly sales, the company could forecast sales in future months.

2.    Linear regression can also be used to analyze the marketing effectiveness, pricing and promotions on sales of a product

3.    Linear regression finds application in a wide range of environmental science applications. In Canada, the Environmental Effects Monitoring Program uses statistical analyses on fish and benthic surveys to measure the effects of pulp mill or metal mine effluent on the aquatic ecosystem.

4.    Correcting errors: Even the most informed and careful managers do make mistakes in judgment. Regression analysis helps managers, and businesses in general, recognize and correct errors. Suppose, for example, a retail store manager feels that extending shopping hours will increase sales. Regression analysis may show that the modest rise in sales might not be enough to offset the increased cost for labor and operating expenses (such as using more electricity, for example). Using regression analysis could help a manager determine that an increase in hours would not lead to an increase in profits. This could help the manager avoid making a costly mistake


APPLICATION OF REGRESSION ESTIMATOR WITH R CODE


DATA DESCRIPTION:

Here We select a random sample using the SRSWOR procedure of 59 corona cases data set of Kerala from a population of 1000 cases. He collected information about the Confirmed Indian national and Confirmed Foreign national from the selected states are given below


ANALYSIS











CONCLUSION:

Here the data of Covid-19 is given and we find the results. The estimated population mean 56.07663 that we have obtained is and the Confidence Interval for the Population mean is [55.73403,56.41923]. The population total that we have obtained is 56076.63  and the confidence Interval for the population total is [55734.03,56419.23]. The varience of y_bar using regression is 26973.45.

 

ADVANTAGES OF REGRESSION ESTIMATOR

Regression analysis uses data, specifically two or more variables, to provide some idea of where future data points will be. The benefit of regression analysis is that this type of statistical calculation gives businesses a way to see into the future.

 

DISADVANTAGES OF REGRESSION ESTIMATOR

It is assumed that the cause and effect relationship between the variables remains unchanged. This assumption may not always hold good and hence estimation of the values of a variable made on the basis of the regression equation may lead to erroneous and misleading results.

 


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