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

Multivariate statistical methods, As one of the oldest multivariate stati...

As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived

Root mean square deviation, Root Mean Square Deviation The standard d...

Root Mean Square Deviation The standard deviation is also called the ROOT MEAN SQUARE DEVIATION. This is because it is the ROOT (Step 4) of the MEAN (Step 3) o

Kurtosis and skew, how to interpret results, a good explanation to help me ...

how to interpret results, a good explanation to help me understand.

Calculate the ratio of the sample standard deviation, The Case Study includ...

The Case Study included information about the price for a full meal before and after the law change (in dollars).  Of interest is whether the differences in price for a full meal b

Time series, Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 ...

Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 2012 14 2013 16 Determine the trend from data given above?

HLT 362, What is an interaction? Describe an example and identify the varia...

What is an interaction? Describe an example and identify the variables within your population (work, social, academic, etc.) for which you might expect interactions?

SPSS Program, I have 5 observations that i must plug into spss. I need an e...

I have 5 observations that i must plug into spss. I need an example of 1. I do not know if you are familiar with SPSS but I am going to ask anyway. Subject 1 is a Hispanic male who

Stat, solve problems

solve problems

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