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MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 53: Sample Space, Likelihood Ratios In Diagnostic Testing, Null Hypothesis

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rosi10agarwal
6 Apr 2023
School
Indian Institute of Technology - IIT Kanpur
Department
Mathematics
Course
MTH-416, REGRESSION ANALYSIS
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Document Summary

This equation can be compared with the normal equations comparison yields the following conclusions: X y x xb in the model y x . Ay is the study variables vector in deviation form. 2ax is the explanatory variable matrix in deviation form. This is the normal equation in terms of deviations. Its solution gives ols of slope coefficients as b. The estimate of the intercept term is obtained in the second step as follows: Now we explain various sums of squares in terms of this model. The expression of the total sum of squares (tss) remains the same as earlier and is given by. Ss res where the sum of squares due to regression is. Ss e e and the sum of squares due to residual is. There are several important questions which can be answered through the test of hypothesis concerning the regression coefficients. Which specific explanatory variables seem to be important? etc.

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Related Questions

First photo is the main question, the example is shown in the other photo.

Solve the system of equations.
 
 
Select the correct choice below and fill in any answer boxes within your choice.
A. The one solution is x = ____, y = ____, and z = ____. (Simplify your answers.)
B. There are infinitely many solutions. If z is allowed to be any real number, then x= ____ and y = ___ (Type expressions using z as the variable.)
C. There is no solution.
 
Solve the system of equations.
 
 
 
To eliminate the x-item from the second equation. Multiply both sides of the first equation by - 1 and add the result to the second equation.
 
     
Now use the sarse method so eirrinale the x-term in the third equation
Multiply both sides of the first equation by -1 and add the result in the third equation.
 
 
 
The equivalent system with the new second and third equations is shown below. The next step is to eliminate the y-term from the third equation.
 
     
 
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Finally, to obtain an x-coefficient of 1 in the this equation multiply both sides of the third equation by  
 
 
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The third equation gives the value of a
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Using Inverse Matrices to Solve a System Express the system of linear equations as a matrix equation. Then solve the matrix equation by multiplying each side by the inverse of the coefficient matrix.