First assumption behind least squares: Ax = b- (noise e with mean zero). Multiply the error vectors e = b - Ax by (AT A)-1AT to get x - x on the right. The estimation errors x -x also average to zero. The estimate x is unbiased.

Q: (3) Sketch the points (−1+ ei)¹/5 and (-1 - ei)¹/5 for € "small". Based on your sketch, explain why…

A: (3) The given points are -1+εi15 and -1-εi15 for small ε.      We know logz=logz+iArgz   for z≠0,…

Q: For each of the following, if the statement about a topological space is always true, prove it;…

A: Hence prove that boundary of a closed set is closed in topological space.

Q: An observer at a busy bus stop did a 30-minute study of 3 buses. Given the following -Alight time…

A: In this problem, we are given data on three buses that arrived at a busy bus stop during a 30-minute…

Q: This exercise provides an example of a function f: R² → R such that all first partial derivatives…

A:

Q: Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

A:

Q: Prove that • Ụ ( ¹⁄2, ¹ − ¹ ) = (0, 1). 72 n>2 ● U ,1 - ¹] = (0, 1). 72 n>2 n (0,1/2) = 6. n>2 • U…

A:

Q: The value of the Conference Board Index of 10 economic indicators in the United States could be…

A: We will solve the question.

Q: Find the area of the surface defined by x + y + z = 1, x2 + 2y2 ≤ 1.

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: Complex numbers (-16)+ z that satisfy

A: Given: Let z=-1614. To Find: Complex number z

Q: 1. A firm decided to raise funds by issuing ₱1,000 bonds a coupon rate of 6% paid semi – annually…

A: Sol:- To calculate the amount that the firm can raise by issuing 10,000 bonds, we need to first…

Q: ∞ 5 Σ (-1)^² (8) converge absolutely, converge conditionally, or diverge? n=1 Does the series…

A:

Q: Show that the set of solutions of a second-order linear homogeneous differential equation is…

A:

Q: Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., æn) of positive integers…

A: The Catalan numbers are a sequence of integers that appear in many combinatorial problems. One of…

Q: Solve the following first-order differential equation by first finding the integrating factor: x^2…

A:

Q: The total cost (in dollars) of producing x food processors is C(x) = 2400+80x-0.3x². (A) Find the…

A: Given that The total cost (in dollars) of producing x food processors isCx=2400+80x-0.3x2

Q: Consider the following decision matrix: A B C $1 > 5 3 4 Select all the following that are true: $2…

A:

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

A: Here,  we have to find the radius of convergence amd check the behavior of series,  i. e.  Whether…

Q: Which of the following are true for the matrix A in reduced row echelon form (there is no augmented…

A:

Q: 22. Evaluate the Laplace Transform of * L{e-2t+4e-3t) Option 1 Option 3 5s + 11 (s+2)(s+3) 5s + 11…

A:

Q: An unbiased coin is tossed four times. Find the probability of the given event. (Enter your answer…

A:

Q: a) A = B = R and f+g: R → R is defined by (f + g)(x) = f(x) + g(x); b) A = B = R and fg: R → R is…

A:

Q: Assume that A, B are square matrices and that AB is invertible. If AB = I, show that B is…

A:

Q: 8. Given the space curve C as the image of the vector valued function r(t) = 2ti+t³j+-t-¹ k OR r(t)…

A:

Q: Let band c be constants. (1) Suppose that a²+bx+c = 0 has no solutions. (1A) What is the solution to…

A:

Q: Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal…

A: Given that Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal…

Q: Estimate ³ dx using SIMP(2), which is the same as $4. S₁ x³ dx ≈ 3 Submit answer

A:

Q: Solve the following first order differential equation: x dy/dx sin (y/x) = y sin (y/x) - x  using…

A:

Q: Find the upward flux of F= (14e2,-7e²,-6) through the first-octant part of the triangle a+2y+3z-6.…

A:

Q: - a) Evaluate (3 – 6xy)dA where D is the region shown below.

A: According to guidelines we can do only first question. We have to find the area of shaded region…

Q: Determine the local maximum and minimum values and saddle point (s) of the function. (1) f(x,y) =…

A: ( 1 )                      Given              f(x,y) = x-y e-x2-y2                           fx =…

Q: 6. Let u(x, y) = Re(2²) and v(x, y) = Im(2²). Compute the line integrals in R² given by (udx - vdy)…

A:

Q: What is the x value given the following information: z=-2.26 = 77.34 σ=2.46 *Round your answer to…

A: The value of x

Q: If the Taylor series of function f(x) = In(4x + 3) about a = 1 is co + (x - 1)" then, and if n ≥ 1,…

A:

Q: Solve the system 21 X2 X3 = +8 -2 +4x3 = 3x12x2 +6x3 = -5 2x1 -4x3 = 6 21

A:

Q: Write the slope of a line parallel to this one. y=8-3x

A:

Q: Solve the following LPP Maximize Z = 2 x1 +5x2 subject to the conditions x1+ 4x2 ≤ 24 3x1+x2 ≤ 21…

A:

Q: Consider the boundary value problem y" + 4y = 0, 0≤x≤ b, Find choices for b and B so that the…

A:

Q: The curves 7₁(t) = (4t, t², 5t6) and F₂(t) = (sin(—t), sin(4t), t — π) intersect at the origin. ㅠ…

A:

Q: a) Graphs G and H are isomorphic. Give an isomorphism from G to H as described in lecture notes 2.1:…

A: As per the question we are given three non planner graphs ?, ℍ, ? and we have to prove that : The…

Q: 5. The boundary value problem y" + 3y' = 2y +2x+3, 0≤x≤ 1, y(0) = 1, y(1) = 3. (a) Write out the two…

A: Given: A boundary value problem y''+3y'=2y+2x+3  , 0≤x≤1 , y0=1 , y1=3 . To Find :  a) Write out the…

Q: Let A ∈ Rm×n and B ∈ Rn×r . Show that ||Ax||2 ≤ ||A||(1,2)||x||1 for all x in Rn.

A: To prove that ||Ax||2 ≤ ||A||(1,2)||x||1 for all x in Rn, we can use the Cauchy-Schwarz inequality.…

Q: Decide whether the following sets of vectors span the given vector space, are linearly independent…

A:

Q: 2. Use the Equational-style to prove the following: a. AVB AV¬B=A b. HAVAAB = A c. d. AV (BA) B → A…

A:

Q: 1. Use Fundamental Theorem of Calculus to evaluate (a) Jo sin zdz, C: arc eit, -≤ t ≤ 5; (b) Jedz,…

A: To Evaluate: The following integrals using Fundamental theorem of calculus: (a) ∫Csinz dz ,  C: eit,…

Q: 4g - 2x2 + 5% -1- Σακ(π)κ. 4x4 k>0 b) -(m)2 + (r)1 + 6 = Σb k>0

A:

Q: 0.0139 0.0055 0.0028 Let D = 0.0055 0.0111 0.0055 be a flexibility matrix, with flexibility measured…

A:

Q: SOLVE FOR the differential equations 15) (2x - 5y + 12) dx + (7x - 4y +15) dy = 0

A:

Q: Count how many ways you can move a point on a grid while only moving it one unit up or to the right…

A: Sol:- We can solve this problem using the principle of inclusion-exclusion and graph theory. First,…

Q: Which of the following are true for the matrix A in reduced row echelon form (there is no augmented…

A: Solution:

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.