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

Mode, Mode The mode is the value which occurs most frequ...

Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste

Statistics assignment, To compare three brands of computer keyboards, four ...

To compare three brands of computer keyboards, four data entry specialists were randomly selected. Each specialist used all three keyboards to enter the same kind of text material

Skewness, Skewness Meaning and Definition  Literal meaning of skew...

Skewness Meaning and Definition  Literal meaning of skewness is lack of symmetry; it is a numerical measure which reveals asymmetry of a statistical series. According t

Regression lines, Regression Lines It has already been discussed that t...

Regression Lines It has already been discussed that there are two regression lines and they show mutual relationship between two variable . The regression line Yon X gives   th

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

how to analyzePractice-Based Evidence Back to the Future

Solve linear programming problem using the simplex method, Question: (a...

Question: (a) Shale Oil, located in the island of Aruba, has a capacity of 600,000 barrels of crude oil per day.  The final products from the refinery include two types of unle

Show the hypothesis test, The file Midterm Data.xls has a tab labeled "Inc...

The file Midterm Data.xls has a tab labeled "Income Data 2009". This data is collected income data from a sample of 400 people in 2009. Use a hypothesis test to see whether the av

Age at first marrage, get a questionnaire that captured age at first marria...

get a questionnaire that captured age at first marriage

Weight distribution, What does the confidence level of a confidence interva...

What does the confidence level of a confidence interval tell you? Suppose that a population has mean, µ, and standard deviation, σ.  What does the central limit theorem tell us

Weibull distribution, slope parameter of 1.4 and scale parameter of 550.cal...

slope parameter of 1.4 and scale parameter of 550.calculate Reliability, MTTF, Variance, Design life for R of 95%

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