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 Ex '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

Bernoulli''s theorem, Bernoulli's Theorem If a trial of an experiment c...

Bernoulli's Theorem If a trial of an experiment can result in success  with probability p and failure with probability q (i.e.1-p) the probability of exactly r success in n tri

Regression, why we use dummy variable

why we use dummy variable

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

Difference in goals between pca and fa, In PCA the eigknvalues must ultimat...

In PCA the eigknvalues must ultimately account for all of the variance. There is no probability,'no hypothesis, no test because strictly speaking PCA is not a statistical procedure

Probability, 1 A penny is tossed 5 times. a. Find the chance that the 5th t...

1 A penny is tossed 5 times. a. Find the chance that the 5th toss is a head b. Find the chance that the 5th toss is a head, given the first 4 are tails.

X-bar charts, First we look at these charts assuming that we know both the ...

First we look at these charts assuming that we know both the mean and the standard deviation of the process, that is  μ and  σ . These values represent the acceptable values (bench

Data project, Dr. Jim Mirabella UNIT EIGHT: DATA ANALYSIS PROJECT All Excel...

Dr. Jim Mirabella UNIT EIGHT: DATA ANALYSIS PROJECT All Excel output should be copied into a single Word document where you must enter all of your responses to the questions below.

Schedule, Schedule Schedule is also used for the collection of primary ...

Schedule Schedule is also used for the collection of primary data. A schedule is a list of question. it is a device of obtaining answer to the questions in a form which is fill

Predict higpa using a logistic regression, In this problem, we use the CSDA...

In this problem, we use the CSDATA data set, which is available in 'CSDATA.txt'. We do ne an indicator variable, say HIGPA, to be 1 if the GPA is 3.0 or better and 0 other- wise. S

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