Assumptions in regression, Applied Statistics

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
Posted Date: 9/15/2012 5:05:34 AM | Location : United States







Related Discussions:- Assumptions in regression, Assignment Help, Ask Question on Assumptions in regression, Get Answer, Expert's Help, Assumptions in regression Discussions

Write discussion on Assumptions in regression
Your posts are moderated
Related Questions


Motion Picture Industry (95 Points) The motion picture industry is a competitive business. More than 50 studios produce a total of 300 to 400 new motion pictures each year, and t

Purposive or Judgement Sampling Under this method of sampling, the choice  of selection of sample  items from the universe  depends exclusively on the judgement  of the investi

practical application of standard error

Ask queFrom these studies, which of the following may be considered a variable that can have a probability distribution? [I] Percentage of Sub-Saharan Africans that smoke [II] Perc

What is a null hypothesis? ..

Arithmetic Average or Mean The arithmetic mean is the most widely and the most generally understandable of all the averages. This is clear from the reason that when the term

how to get statistical quality control assignment in brief?

You will recall the function pnorm() from lectures. Using this, or otherwise, Dteremine the probability of a standard Gaussian random variable exceeding 1.3.  Using table(), or