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

Chi square test, who invented the chi square test and why? what is central ...

who invented the chi square test and why? what is central chi square and non central chi square test? what is distribution free statistics? what are the conditions when the chi squ

Sensitivity and Specificity tests, The prevalence of undetected diabetes in...

The prevalence of undetected diabetes in a population to be screened is approximately 1.5% and it is assumed that 10,000 persons will be screened. The screening test will measure

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 gaussian random variable , You will recall the function pnorm() fr...

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

Find the rank correlation coefficient, 1. Calculate the mean and mode of: ...

1. Calculate the mean and mode of: Central size 15 25 35 45 55 65 75 85 Frequencies 5 9 13 21 20 15 8 3 The following data shows the monthly expenditure of 80 students of

Normal distribution, Normal Distribution Meaning: According  to ya Lu...

Normal Distribution Meaning: According  to ya Lun Chou  There perfectly smooth and symmetrical  curve, resulting  from the expansion of the binomial (p+q) n    when n approac

Principles of data analysis, For the data analysis project, you will addres...

For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class.   You choose the questions; you decide h

Calculate the seasonal indexes , The total number of overtime hours (in 100...

The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hour

Choose the correct null hypotheses, For the following claim, find the null ...

For the following claim, find the null and alternative hypotheses, test statistic, P-value, critical value and draw a conclusion. Assume that a simple random sample has been selec

Interpolation and extrapolation, Meaning of Interpolation and Extrapolation...

Meaning of Interpolation and Extrapolation Interpolation is a method of estimating the most probable  missing figure on  the basis of given data under certain assumptions. On t

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