What is the purpose of principal component analysis? Given the covariance matrix of order 2× ,2 explain how would you extract the principal components. Also, explain how would you find the proportion of total population variance for all the principal components.
Principal Component Analysis (PCA) is a statistical technique used in the field of probability and statistics for dimensionality reduction while preserving as much variability in the data as possible. The main objective of PCA is to transform a set of possibly correlated variables into a smaller number of uncorrelated variables called principal components. These components are ordered in such a way that the first few retain most of the variation present in all of the original variables. This is particularly useful when dealing with high-dimensional data, as it simplifies analysis and visualization, reduces noise, and helps in identifying patterns.
PCA works on the principle ________ _____ _______ __________ _____ _________ ____ ________.
________ _______ __________ _______ __________ ______ ____ ___ _______ __________ ______ _______.
________ _____ ____ _________ __________ _______.
_________ _________ ________ _____ _____ _____ ______ ________ _______ _______ __________.
_____ _________ _________ ______ _______ ______ ______ _______.
________ _______ ____ _______ ____ ___ _________ ______ ___.
__________ __________ ___ ________ ________ __________ __________.
________ ____ ____ _____ _____ ____ _________ ___ __________ ____.
________ ___ _________ ________ ___ ________ ________.
_____ _____ _________ ________ ________ ________ ________ ______ ______ __________ __________.
________ ______ __________ ________ ______ _________ _____ _______.
__________ __________ ____ __________ ____ ___ ____ ______ ______.
_______ ___ ____ ___ _______ _______ ______ _________ ______ ___ ___.
___ ___ ___ __________ _____ ____ ____ _____ ______ _______ _______ ________.
________ _______ ____ _____ __________ ___ _____ ______ _________ _________ _______.
_________ _______ ____ ______ _____ ______ ____ ________ _______ _____ ___ _____.
_____ _____ ______ ________ ________ ______ ________.
_________ _________ __________ __________ ___ ___.
__________ __________ _______ ___ ______ _____ __________ ____ _______ ___ ________.
_________ ________ _____ ________ _________ ___ _______.
________ ____ ____ _______ __________ __________.
_______ ________ ________ __________ ________.
_____ ___ ____ ___ ________ ___ ________.
_____ _______ _________ _________ _______ ______.
_________ ___ __________ __________ _______ ______.
______ ________ _____ ________ _______.
_________ ____ _________ ____ __________.
_______ ______ ________ _____ ___ ______ _____.
__________ _____ _________ __________ _______ _________.
__________ _______ _____ ______ _________.
_____ ______ ____ ____ ________ ______ ____ ________.
____ ________ _________ _____ ____ __________ ______ _______ ________ _____ _____ ______.
______ __________ ______ __________ ________ ___.
__________ ___ __________ _______ ___ _____ _______ _________.
_________ _______ ______ _______ ___ ____ ______.
________ _________ ____ ____ ______ ____ ____ ____.
_____ ________ ______ ________ _________ ___.
______ __________ _______ __________ _____ __________ _____ _________ ________ ______.
____ ______ ____ _________ __________ __________ ____ __________ ______.
_____ ________ _______ __________ _______ _____ _____ ___ ________.
_________ ____ ________ _____ ________ ________ __________ ____ ______ _____ _____.
______ ____ ___ ________ _________ ________ _______.
______ ________ _________ ___ _________ ______ _________ ______.
______ ____ ________ _____ ______ _____ ___ ________ ___ _________ _________.
______ ___ _______ _________ ________ ____ _________.
______ __________ ________ _______ _______ ______ ________.
___ ___ ______ ________ ___ _____ _____.
_________ __________ _____ ____ __________ _________ ________ ____ _________ _______.
_____ _____ _________ __________ _____ ________ __________ _________ ____ _________.
_______ ______ ____ ______ ______ _______.
________ _________ _________ __________ _________ ____ __________ ___ _____.
Get Full Answer on WhatsApp
In an investigation related to a specific type of scores of men and women aged 65 to 70, the mean verbal and performance scores for 101 subjects were found to be:
The sample covariance matrix of the scores was
In order to test the null hypothesis that observations came from a population with mean
apply a suitable test statistic. You may consider α = 01.0 for the test.
A study about a population showed that the mobility of population of a state to a village, town and city is in the following percentages:
| From | To | ||
| Village | Town | City | |
| Village | 60 | 25 | 15 |
| Town | 10 | 70 | 20 |
| City | 10 | 30 | 60 |
For the (M/M/K) : (∞ / FIF )0 queuing model with arrival rate λ and service rate per service channel µ, obtain the steady-state probability of n customers in the system, P . n Hence or otherwise, find the probability that an arrival has to wait.
What is branching process? Give two real examples of branching process.
If P(s) and Pn(s) respectively is the probability generating function (pgf) of the i.i.d. random variables and the random variables {Xn}, where Xn+1 =
Then show that:
Pn(s) = Pn-1(P(s))
and Pn(s) = Pn-1(P(s)).
What is branching process? Give two real examples of branching process.
If )s(P and P )s( n respectively is the probability generating function (pgf ) of the i.i.d.
random variables and the random variables
Then show that:and
A study about a population showed that the mobility of population of a state to a village, town and city is in the following percentages:
| From | To | ||
| Village | Town | City | |
| Village | 60 | 25 | 15 |
| Town | 10 | 70 | 20 |
| City | 10 | 30 | 60 |
In order to fit the regression line on a data set consisting of 34 pairs of values (z,y), the least square estimates of β1 and β2 are to be computed. From the data set, the following values are obtained:
Obtain the fitted regression line.