MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 26: Indian Institute Of Technology Kanpur, Diagonal Matrix, Generalized Inverse

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rosi10agarwal

6 Apr 2023

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Indian Institute of Technology - IIT Kanpur

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Mathematics

Course

MTH-416, REGRESSION ANALYSIS

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One may search for some relevant prior information about the regression coefficients. This may lead to the specification of estimates of some coefficients. The more general situation includes the specification of some exact linear restrictions and stochastic linear restrictions. The procedures like restricted regression and mixed regression can be used for this purpose. The relevance and correctness of information play an important role in such analysis, but it is challenging to ensure it in practice. For example, the estimates derived in the u. k. may not be valid in india. Then can be k , then the generalized inverse can be used to find the inverse of: employ generalized inverse. In such a case, the estimates will not be unique except in the case of use of moore-penrose inverse of. X x different methods of finding generalized inverse may give different results.

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What are the missing information on the blanks to complete the following?

(a) To define the inverse sine function, we restrict the domain of sine to the interval __________________.

On this interval the sine function is one-to-one, and its inverse function is defined by .

For example, because .

(b) To define the inverse cosine function, we restrict the domain of cosine to the interval __________________.

On this interval the cosine function is one-to-one, and its inverse function is defined by .

For example, because .

carminebeaver375

Average price per square foot of floor area in new one-family houses sold. Price per square foot of floor area excludes value of improved lot Source: Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Price per square foot $55.18 $57.41 $60.21 $62.45 $64.38 $66.81 $67.83 $67.70 $70.43 $71.93 $75.68 $79.21 $85.13 $90.63 $91.99 Instead of working on portions of the scatter plots, we want to approximate the data by a line we can use to predict prices in the future. The line that will best fit the given data is called the linear regression. The approximation will be acceptable whether the determina- tion coefficient R (r**2) is close to 1 or the correlation coefficient r is close to -1 or +1.

a) using your entered data to find the equation y = ax + b of the best line through the data points and give the values of coefficients a and b, and of the determination coefficient R or correlation coefficient r.

b. Use Excel to plot the scatter plot and the regression line on the same graph.

c. Is the linear regression a visually good approximation of the data? Sustain your argument by a mathematical proof.

d. use the linear regression to predict the price per square foot area in 2009 e. In what year will the price per square foot be greater than $199?

sangriaelk229

Question 4,please.and can you give the very detailed steps of the answer

MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 26: Indian Institute Of Technology Kanpur, Diagonal Matrix, Generalized Inverse

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