Assumptions in regression, Applied Statistics

Assignment Help:

Assumptions in Regression

To understand the properties underlying the regression line, let us go back to the example of model exam and main exam. Now we can find an estimate of a student's main exam points, if we also know his or her points on the model exam. As we have stated, a student with score of 85 in the model exam should receive points for the main exam in the vicinity of 75 to 95.

If we knew the model exam scores of all students along with their main exam scores, we would then have the population of values. The mean and the variance of the population of the model exam would be μx and σx2 and respectively. The measurements for the main exam points are  μy  and  σy2 .

The assumptions in regression are:

  1. The relationship between the distributions X and Y is linear, which implies the formula E(Y|X=x) = A + Bx at any given value of X = x.

  2. At each X, the distribution of Yx is normal, and the variances  σx2  are equal. This implies that E's have the same variance,  σ2.

  3. The Y-values are independent of each other.

  4. No assumption is made regarding the distribution of X.

    Since we do not have all of the students' course points and main exam points we must estimate the regression line E(Y|X = x) = A + BX.

    The figure shows a line that has been constructed on the scatter diagram. Note that the line seems to be drawn through the collective mid-point of the plotted points. The term  2148_simple linear regression.png  is the estimate of the true mean of Y's at any particular X = x.

    Figure 8

    682_assumptions in regression.png

Related Discussions:- Assumptions in regression

Case # 2 , Case Problem: A Bipartisan Agenda for Change In a study conducte...

Case Problem: A Bipartisan Agenda for Change In a study conducted by Zogby International, more than 700 New Yorkers were polled to determine whether the New York state government w

Determine the regression equation, The file Midterm  Data.xls has a tab lab...

The file Midterm  Data.xls has a tab labeled "National Grid vs. Alcoa" which presents historical price data for two stocks.  Using the National Grid price as the X-value and the Al

Statistical errors, Statistical Errors              Statistical data ar...

Statistical Errors              Statistical data are obtained either by measurement or by observation. Hence to think of perfect accuracy is only a delusion or a myth, It is no

Sampling, Sampling A  Population  is a collection of all the data point...

Sampling A  Population  is a collection of all the data points being studied. For example, if we are studying the annual incomes of all the people in India, then the population

Decision making ., it is said that management is equivalent to decision mak...

it is said that management is equivalent to decision making? do you agree? explain

Principles of data analysis, For the data analysis project, you will addres...

For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class.   You choose the questions; you decide h

Latin Square design, what is the the Latin Square design? What is its appli...

what is the the Latin Square design? What is its application in research? please explain this term with very simple but with detailed explanation for effective understanding. I hav

HLT 362, What is an interaction? Describe an example and identify the varia...

What is an interaction? Describe an example and identify the variables within your population (work, social, academic, etc.) for which you might expect interactions?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd