a) (This is the first part of Question 3.1.5 from the textbook.) Consider the followingdata:tiYi1.01.1W₁ =Set up the problem of minimization associated with least squares for a best fitline for this data.b) Let1.5 2.0 2.5 3.01.2 1.3 1.3 1.41W2=33-19and w3=6201be vectors in R4. Apply the classical Gram-Schmidt process to find an orthonor-mal basis for the subspace spanned by w₁, W2, and w3.

As per Bartleby rules . When there are 2 different questions. We have to answer only first…

Answered: a) (This is the first part of Question…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 34EQ

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2) Find a least squares quadratic curve to the following datą: 1 2 3 1.7 1.8 2.3 X y 4 3.2
Which of the following best describes the least-squares line fit to the data shown in the plot? (i) bo = 0, bị =-1 (ii) bo = -3, b₁ = 1 (iii) bo-5, b₁ = 2 (iv) bo = −3, bị =-1 (v) bo = 0, b₁ = -3 2 X
Each of the following pairs represents the number of licensed drivers (X) and the number of cars (Y) for seven houses in my neighborhood: Drivers X Cars Y 5 4 5 3 2 2 2 2 3 2 1 1 2 2 Construct a scatterplot to verify a lack of pronounced curvilinearity. Determine the least squares equation for these data. (Remember, you will first have to calculate r, SSy, and SSx) Determine the standard error of estimate, sy|x, given that n = 7. Predict the number of cars for each of two new families with two and five drivers.
a. Rewrite the data points (2,1), (4,2), (8,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal? b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y =B₁ + B₁x², * where x = x-5.75.
a. Rewrite the data points (3,1), (6,3), (7,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal? b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y = Bo + B1x, where x =x- 6.25. a. The data in mean-deviation form are (Type ordered pairs. Use a comma to separate answers as needed.) The associated design matrix, X, isO. Therefore, the columns of X are orthogonal because (Simplify your answer. Use ascending order.) b. Write the normal equations for the data from part (a). Select the correct choice below and fi (Simplify your answer.) the entries in one column are all 1 and the entries in the other column sum to 0. O A. the entries in one column are all 1 and the entries in the other column sum to - 1. О в. one column contains all zeros. The least-squares line, y = Po + B,x* , is y = O:x- 6.25).
a. Rewrite the data points (2,1), (4,2), (8,6) and (9,6) with new x-coordinates in mean-deviation form. Let X be the associated design matrix. Why are the columns of X orthogonal? b. Write the normal equations for the data in part (a), and solve them to find the least-squares line, y =B₁ + B₁x², where x = x-5.75. The associated design matrix, X, is 1 - 1.75 2.25 3.25 1 the entries in one column are all 1 and the entries in the other column sum to 0. (Simplify your answer. Use ascending order.) B. Therefore, the columns of X are orthogonal because b. Write the normal equations for the data from part (a). Select the correct choice below and fill in the answer boxes within your choice. (Simplify your answer.) O A. [Bo B₁] = Bo 421-0
a) Use a calculator or computer to find the least squares regression line, y = mx + b, where the dependent variable y denotes the number of hours of TV watched as a function of IQ, x. Enter the equation for the line below. "b) What is the correlation coefficient of the regression line? Enter r accurate to at least three decimal places.)
Suppose the least squares regression line for predicting weight (in pounds) from height (in inches) is given by Weight= -110+3.5*(height) Which of the following statements is correct? l. A person who is 61 inches tall will weigh 103.5 pounds ll. For each additional inch of height, weight will decrease on average by 3.5 pounds. lll. There is a negative linear relationship between height and weight. a) l and lll only b) l and ll only c) ll only d) l only e) ll and lll only
4. Determine the equation of the least-squares approximating line that is the best fit for the data points (2, 6), (0, 2), and (1, 1).
When developing an exam schedule, the following data were collected from the grade 12 students: 90 students study Advanced Functions 42 students study Math of Data Management 53 students study Calculus & Vectors 23 students study Advanced Functions and Math of Data Management 25 students study Calculus & Vectors and Advanced Functions 15 student study Math of Data Management and Calculus & Vectors 8 students study all three grade 12 math courses 79 students did not study any of these grade 12 math courses How many students were studying exactly two of the grade 12 math courses? 47 39 55 63
2. (a) Find the line of best fit for the data points (-1,-4), (0, -1), (1, 2) and (3,8) and the least square error.
Consider the following table of points in the plane: Fit a straight line to the data in the above table by the least squares method ( Work with two decimal digits)

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