(ii) To make a trend analysis of six evenly spaced data points, one can use orthogonal polynomials with respect to evaluation at the points t = -5,-3,–1,1,3 and 5 (5) (a) Show that the first three orthogonal polynomials are po(t) = 1, p,(t) = t and p2(t) =

(ii) To make a trend analysis of six evenly spaced data points, one can use orthogonal polynomials with respect to evaluation at the points t = -5,-3,–1,1,3 and 5 (5) (a) Show that the first three orthogonal polynomials are po(t) = 1, p,(t) = t and p2(t) =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

(ii) To make a trend analysis of six evenly spaced data points, one can use orthogonal polynomials
with respect to evaluation at the points t = -5, –3, –1,1,3 and 5
(5)
(a) Show that the first three orthogonal polynomials are po(t) = 1, p,(t) = t and p2(t) =
2,2 _ 35
(b) Fit a quadratic trend function to the data
(-5,1), (-3,1), (–1,4), (1,4), (3,6), (5,8).

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