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

Econometrics, Ask question From the household budget survey of 1980 of the...

Ask question From the household budget survey of 1980 of the Dutch Central Bureau of Statistics, J. S. Cramer obtained the following logit model based on a sample of 2820 househol

Hi, i want assignmrnt help

i want assignmrnt help

Correlation coefficients, What type of correlation coefficient would you us...

What type of correlation coefficient would you use to examine the relationship between the following variables? Explain why you have selected the correlation coefficients. A. Re

Statisttics., Explain any two applications of statistics

Explain any two applications of statistics

Stratified random sampling, Stratified Random Sampling: This method of ...

Stratified Random Sampling: This method of sampling is used when the population is comprised of natural subdivision of units, The method consist in classifying the population u

Types of cost-reimbursable contracts, Types of cost-reimbursable contracts ...

Types of cost-reimbursable contracts are:   Cost Plus Fixed Fee contract (CPPF): Compensation is based on a fixed sum independent of the final project cost. The customer a

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

how to analyzePractice-Based Evidence Back to the Future

Arithmetic mean, Arithmetic Mean   The process of computing Arithmetic M...

Arithmetic Mean   The process of computing Arithmetic Mean in the case of individual observations is to take the sum of the values of the variable and then divide by the number

MEASURING TREND, DISCUSS THE METHODS OF MEASURING TREND

DISCUSS THE METHODS OF MEASURING TREND

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