For Problems 67-68, apply the Gram-Schmidt process to the given subset of S of the inner product space V to obtain an orthogonal basis for span (S). Feel free to do arithmetic and calculus calculations on a calculator or computer. Do make it clear, however, where ecach vector in your orthogonal basis came from, and clearly state your answer. 67. V = R“, with the standard inner product, S = {(1,0,1, 1), (1, 1,0, 1), (1, 1, 1,0)}. %3D 68. V = C[0, 1], with inner product (f, 9) = | 5(t)g(t) dt, S={1,r²,1'}.
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.
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![For Problems 67 68, apply the Gram-Schmidt process to the given subset of S of the inner product space V to obtain
an orthogonal basis for span (S). Feel free to do arithmetic and calculus calculations on a calculator or computer.
Do make it clear, however, where ecach vector in your orthogonal basis came from, and clearly state your answer.
67. V = R', with the standard inner product, S = {(1,0,1,1), (1, 1,0, 1), (1,1, 1, 0)} .
%3D
68. V = C[0, 1], with inner product (f, g) = | 5(t)g(t) dt, s={1,r²,x'} .
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fdefaca-e517-410c-b2a6-6a28c51deca0%2F2881948a-f82c-466b-bfde-6c6fe35609c6%2Fy2qf2df_processed.png&w=3840&q=75)
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