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

Evaluation tracking system, BCBSRI was able to reduce MSD related Workers C...

BCBSRI was able to reduce MSD related Workers Compensation cases with lost workdays by implementing a New Ergonomic Program in March 2000 and increasing workstation evaluations. Ex

Determine the subset of variables, Agency revenues. An economic consultant ...

Agency revenues. An economic consultant was retained by a large employment agency in a metropolitan area to develop a regression model for predicting monthly agency revenues ( y ).

Standard deviation, Standard Deviation The main drawback of the deviati...

Standard Deviation The main drawback of the deviation measures of dispersion, as discussed earlier, is that the positive and negative deviations cancel out each other. Use of t

Coefficient of variation, Coefficient of Variation The standard dev...

Coefficient of Variation The standard deviation discussed above is an absolute measure of dispersion. The corresponding relative measure is known as the coefficient of vari

Evaluate minimum capability requirement, You are currently working wit...

You are currently working with a supplier who is producing a shaft whose diameter specification is 6.00 ± .003 inches.  Currently, the process is yielding shafts wit

Define the term multicollinearity, Question: (a) (i) Define the term ...

Question: (a) (i) Define the term multicollinearity. (ii) Explain why it is important to guard against multicollinearity. (b) (i) Sometimes we encounter missing values

Box plots, This box plot displays the diversity wfood; the data ranges from...

This box plot displays the diversity wfood; the data ranges from 0.05710 being the minimum value and 0.78900 being the maximum value. The box plot is slightly positively skewed at

Standard deviation and variance, Explanation of standard deviation and vari...

Explanation of standard deviation and variance Describe the importance of standard deviation and variance, what they calculate and why they are required. Importance of char

Calculation for continuous series or grouped data, Calculation for Continuo...

Calculation for Continuous Series or Grouped Data = where, m = mid-point of class   =

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