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

Statistical process control, Statistical Process Control The variabilit...

Statistical Process Control The variability present in manufacturing process can either be eliminated completely or minimized to the extent possible. Eliminating the variabilit

Statistical keys, Statistical Keys To do statistical o...

Statistical Keys To do statistical operations we must first set the calculator on SD mode [SD stands for "standard deviation" which is the usual st

Lorenz curve , Lorenz Curve   It is a graphic method of measur...

Lorenz Curve   It is a graphic method of measuring dispersion. This curve was devised by Dr. Max o Lorenz a famous statistician.  He used this technique for wealth it i

Evaluate the standard deviation, Use only the rare event rule, and make sub...

Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consis

Utility index , If the economy does well, the investor's wealth is 2 and if...

If the economy does well, the investor's wealth is 2 and if the economy does poorly the investor's wealth is 1. Both outcomes are equally likely. The investor is offered to invest

Practice-Based Evidence, how to analyzePractice-Based Evidence Back to the ...

how to analyzePractice-Based Evidence Back to the Future

Calculating 40th percentile in ogive graph, how do i determine the 40th per...

how do i determine the 40th percentile in an ogive graph

Probability, In 120 tosses of a coin, 45 heads and 75 tails are observed. ...

In 120 tosses of a coin, 45 heads and 75 tails are observed. Is this a balanced coin? Use a=0.05. (Follow the basic steps of hypothesis testing)

Redundancy analysis, In reduced rank regression (RRR), the dependent var...

In reduced rank regression (RRR), the dependent variables are first submitted to a PCA and the scores of the units are then used as dependent variables in a series of

Compare the t interval with the bootstrap interval, Jocko's Garage has been...

Jocko's Garage has been accused of insurance fraud. Data on estimates made by Jocko and another garage were obtained for 10 damaged vehicles (available in 'jockogarage.txt'). Here

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