Suppose that we have measured four data points (1,1,1), (1,2,0), (3,-1,0), (0,0, 1) and the our model asserts that the points should lie on a single plane not passing the origin. Use least squares method to find a best approximation of the plane. [10]

Q: 6. [8.5] Consider the points A(1, 3, 1), B (2, 1, 0), and C(5, 1, 1). Determine the Cartesian…

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Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (-1,-1,1),…

A: Let Put the given points in f we have Now, we have minimize this function.

Q: Find the parabola y = ax2 + bx + c that best fits the four points (0,0),(1,2),(2,3),(-1,1) by the…

A: Step 1:Step 2:  Step 3: Step 4:

Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (3, -1, 1), (1,…

A: Data points 0,-4 , 0 ,5 , 0 ,0 ,3 , -1 , 1 ,1 , -2 ,1 ,1,-5 , -3. To Find: The plane z=a+bx+cy that…

Q: Find an equation of the plane that is parallel to the line of intersection of the planes x-y+ 2z = 3…

A: To find an equation of the plane that is parallel to the line of intersection of the planes x - y +…

Q: Q3/ Find the equation of the plane that contains the line 3-x 2+y %3D 3 - z, and the point P (1, 4,…

A: Given line is  3-x4=2+y2=3-zand the point is (1,4,3) find the equation of the plane

Q: I find the equation of the plane passing through the three point. (1,2,3) (2,-3, 4), (1,1,7),

A: We have to find a equation of plane passing through the given three points.

Q: Find the least squares approximating parabola for the given points. (1, 3), (2, −4), (3, 6), (4, 9)

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Q: Let B {(1,2,3), (3, 2, 1), (0,0, 1)}. Show that B is linearly independent and spans R. Show all of…

A: In this question, concept of linear span is used. Linear spanLet V represent a vector space, and…

Q: Ar+By+C Derive the normal equations for finding the least-squares plane z for the N points (x1, Y1,…

A: We are given a set of N points x1, y1, z1,...,xN, yN, zN and we have to derive the normal equations…

Q: 2. Find the equation of the place that pusses + through the point= (-1,2,1) Contains the line of…

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Q: 3. Find an equation for the plane in R³ containing the points P = (4, 1, 0) Q=(3, 2, 1) R = (5, 1,…

A: The given points are, P=(4,1,0)Q=(3,2,1)R=(5,1,1). Let an equation containing three points…

Q: One of the objectives of Simple Linear Regression is finding the values of the intercept (bo) and…

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Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

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Q: Find the point on the plane 3x - 2y + z = 16 that is closest to the point (1,2,3). (Use the method…

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Q: For the data (-3,9), (-2,6), (0,2), and (1,1) find the line and the parabola that provide the least…

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Q: Find the parabola that gives the best least squares approximation to the points: (-1,2), (0, -2),…

A: The problem of finding the parabola that gives the best least squares approximation to a given set…

Q: Compute by hand the natural cubic spline for the data points (2,0), (1, 1), (0, 0).

A: Given data points are: 2 , 0 , 1, 1, 0 , 0. To Find : Natural cubic spline.

Q: 4. Derive the normal equations for finding the least-squares plane z = Ax+By+C for the N points (x1,…

A: The assumption is that the z component of the data is functionally dependent on the x and y…

Q: Find the parabola that gives the best least squares approximati (-1,-1), (0, 1), (1,0), (2, 4).

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Q: Find the linear equation of the plane through the point (0, 1, 1), (1, 0, 1), and (1, 1, O)

A: Consider the point (0,1,1). Take option (a) x-y-z+2=0-1-1+2=0 Take option (b) -x+y-z+2=-0+1-1+2=2≠0…