Regression constants, Applied Statistics

Assignment Help:

The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the total amount will be the smallest possible amount. This criterion is called the Method of Least Squares.

Minimizing the sum of the squared differences of each value of Y from the regression line by the method of calculus, we arrive at two equations, called the normal equations:


343_regression constant.png

Solving these equations simultaneously, and using equivalent expressions for   1028_computation of covariance ungrouped data3.png   and    424_computation of covariance ungrouped data2.png   , we obtain the following formulae used to calculate the coefficients a and b in the regression line  =   1193_simple linear regression.png  = a + bX

         E(Y|X = x) = a + bx     

2242_regression constant1.png 


Related Discussions:- Regression constants

Find out the probability, There are n seats on an airplane and n passengers...

There are n seats on an airplane and n passengers have bought tickets. Unfortunately, the first passenger to enter the plane has lost his ticket and, so he just chooses a seat at r

Measures of dispersion, Other Measures of Dispersion In this section, ...

Other Measures of Dispersion In this section, we look at relatively less used measures of dispersion like fractiles, deciles, percentiles, quartiles, interquartile range and f

Flow chart for confidence interval, Flow Chart for Confidence Interval ...

Flow Chart for Confidence Interval We can now prepare a flow chart for estimating a confidence interval for μ, the population parameter. Figure

Write out the estimator of the linear combination, Now, let's look at a dif...

Now, let's look at a different linear combination. Suppose we are interested n comparing the average mean log income for no college education ( 16). 1. Write out the linear com

Median, The median, as the name suggests, is the middle value of a series a...

The median, as the name suggests, is the middle value of a series arranged in any of the orders of magnitude i.e. ascending or descending order. As distinct from the arithmetic

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

Simple linear regression model, The data le for this assignment is brain-b...

The data le for this assignment is brain-body-wts.txt, which lists the averages brain weights (gm) and body weights (kg) for a number of animal species. Your task is to t an appr

Determine the matrix of the transformation, Consider the linear transformat...

Consider the linear transformation (a) Find the image of (3 , -2 , 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transf

Calculate the damping ratio for each system, (i) Plot the step responses of...

(i) Plot the step responses of the following second order systems and state the nature of each system. For each case, find the poles and plot the location of the poles in the compl

Chi-square test, Consider the following linear regression model:      a)...

Consider the following linear regression model:      a) What does y and x 1 , x 2 , . . . . x k represent?      b) What does β o , β 1 , β 2 , . . . . β k represent?

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