MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 12: Regression Analysis, Indian Institute Of Technology Kanpur, Polynomial Regression

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chemosmart-007

21 Jul 2021

School

Indian Institute of Technology - IIT Kanpur

Department

Mathematics

Course

MTH-416, REGRESSION ANALYSIS

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All

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A model is said to be linear when it is linear in parameters. So the model and are also the linear model. In fact, they are the second-order polynomials in one and two variables, respectively. The polynomial models can be used in those situations where the relationship between study and explanatory variables is curvilinear. Sometimes a nonlinear relationship in a small range of explanatory variable can also be modelled by polynomials. The thk order polynomial model in one variable is given by. 1,2,, k then the model is multiple linear regressions model in k explanatory variables j. 0 x x y x so the linear regression model y x . 2 the techniques for fitting linear regression model can be used for fitting the polynomial regression model. For example: or is a polynomial regression model in one variable and is called a second-order model or quadratic model. 2 are called the linear effect parameter and quadratic effect.

Related Questions

can someone help me from 3 to 6. Thank you.

Can some do this ?

Complete this assignment in Maple. When you are finished, save it to your hard drive and email a copy of your Maple worksheet to me at Write "Math 1204 Lab 4: Name1 and Name2" exactly like this as the subject of your email, where Name1 and Name2 are your names (if you work on this alone, put one name). This lab will get you to construct an interpolating polynomial from given data. Open Maple and load the Linear Algebra package as usual. A chemical company is testing the exothermic properties of a new molecule being combined with 100 ml Hydrochloric Acid at 21 degrees C. Experimentally, they have recovered the following data: Look in your notes for Section 2.7 and remind yourself how polynomial interpolation works. Using MAPLE and our techniques from Section 2.7, find an interpolating polynomial that passes through all six data points. To do this, it might be easier to set each amount of molecule as a variable, like this: and so on. Using this polynomial estimate the temperature of the HCl when 400 mg of the molecule is added 125 mg is added. 50 mg is added. We will now graph the data points and your polynomial on the same graph. First, we need to include the 'plots' package from Maple with the following command: > with (plots); Make a list of your ordered pairs of data and call it K. Example: if I wanted to store the ordered pairs (1, 2) and (6, -1) in a list named K, I would input the following command: > K: [[1, 1], [6, -1]]; Note the MAPLE uses square brackets for ordered pairs, and lists as well. Plot your points with the following command: > pointplot(K); Input your interpolating polynomial into MAPLE and call it f. Plot your interpolating polynomial with the following command: > plot(f, x = 1..6); Note that the second part of the plot function tells MAPLE the bounds for x in our graph. Plot these together on the plot function tells MAPLE the bounds for x in our graph. Plot these together on the same graph in the following way: > display ({pointplote(K), plot(f,x=-1..6)}); What do you notice about your data points in relation to your function? An intern is asked to run the experiment again. They recover the following data. Attempt to use polynomial interpolation for this set of data. Why doesn't work? Explain why there is no function that can model this data.

First, create 3 equations of the form ax+by+cz=d , where a, b, c, and d are constants (integers between – 5 and 5). For example, x + 2y – 2= -1 . Perform row operations on your system to obtain a row-echelon form and the solution. Go to the 3D calculator website GeoGebra and enter each of the equations. After you have completed this first task, choose one of the following to complete your discussion post. 1. Reflect on what the graphs are suggesting for one equation, two equations, and three equations, and describe your observations. Think about the equation as a function f of x and y, for example, x + 2y +1 = 2 in the example above. Geogebra automatically interprets this way, that is, like z=f(x, y)=x+2y+1 , it isolates z in the equation. 2. What did the graphs show when you entered the second equation? 3. Give a simple description of the system x=0 y=0 z=0 x = 0 can be seen as the constant function x=g(y, z)=0y+0z=0 . Of course, you can use GeoGebra to “observe” the system. 4. Give an example with 2 equations as simple as possible with 3 variables (at least 1 being non-linear; keeping z to the one power on both equations) and describe the potential of GeoGebra to study nonlinear systems.

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MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 12: Regression Analysis, Indian Institute Of Technology Kanpur, Polynomial Regression

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