QUESTION 4Consider a set of points in the X-Y plane: (x1.y1) (x2.2) (x3y3) (x4y4) etc. We wish to construct a line in the plane that minimizes the distancebetween each point and the line. There are many ways to do this, but one is the popular Least Squares Method.Let the equation of our line be y=b+mPlug in each point:y₁ =b+mxy₁=b+mx+ mx ₂y₁=b+mxE3=b+ FLX21This is a matrix equation of the form:aM=004X=1xY=XM Y=It turns out that the optimal solution can be shown to be:M=(x¹x)-1X'yQuestion: What is the slope of a least squares approximation to the following data points (1.1.2). (2.2.1) (3, 5.5), (4,8.75). (5,10.3)? Enter youranswer in the space provided rounded to the hundreths place,You may use a software program to assist with the matrix math.

The given points are .The objective is to find the slope of a least square approximation.

Answered: Question: What is the slope of a least…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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In order to study the relationship between age and length of time that a smoker has been smoking, the following data were collected. x= age of a smoker y= years since he or she started smoking. x = y= 26 8 32 9 27 7 24 6 34 10 20 4 Compute the coorelation and find the least squares line.
The cost of a leading liquid laundry detergent in different sizes is given below. Size (ounces) Cost ($) 16 3.59 32 4.39 64 5.19 200 10.19 Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.)ŷ = + x
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Hello there, can you help me solve the problem with two subparts (b and c) Problem: (the image is attached) Subparts: b. Find the least-squares curve of the form above to fit the data (4, 1.57), (6, 2.05), (8, 2.5), (10, 2.7), (12, 3.1), (14, 3.6), (16, 3.8), and (18, 4.35), where x and y represent sales and costs in thousands. Produce a graph that shows the data pts and the graph of the cubic approximation. y = __x + (__)x2 + (__)x3 c. (the image is attached)
Consider the following. x 1 2 3 4 y 4 6 9 13 (a) Find an equation of the least-squares line for the data. (Give each answer correct to 3 decimal places.)y = x +(b) Draw a scatter diagram for the data and graph the least-squares line.
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (c) The printout gives the value of the…
Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:
A student is preparing to take a stand allies exam she was told that she needs to get plenty of sleep the night before the exam she is interested in the relationship between the number of hours of sleep a student gets her for an exam and the score earned on the exam. She collects information from 10 other students who have already taken the exam as shown on the table. she fits at least squares regression line to the data and determines the equation of the line is why equals 26-0.18 X where why is the score earn on the exam and ask is the number of hours of sleep the night before the exam. The residual is given. based on the residual plot is the linear model appropriate? no, there is no clear pattern in the residual plot. yes, there is no clear pattern in the residual plot. no, the student who got the most you've had a negative residual yes, there are more negative residuals (6) then positive residuals (4)
а. Complete the table. (or just write answers) Xi Yi 2 2 3 4 Totals E x; = E yi = Exf = Σχy Find SSxy, SSXX B1. x, y, and fo- Write the equation of the least squares line. b. C. d) What will be y if x=10
Hello there, can you help me solve the problem with two subparts (b and c)? Thank you Problem: (the image is attached) Subparts: b. Find the least-squares curve of the form above to fit the data (4, 1.57), (6, 2.05), (8, 2.5), (10, 2.7), (12, 3.1), (14, 3.6), (16, 3.8), and (18, 4.35), where x and y represent sales and costs in thousands. Produce a graph that shows the data pts and the graph of the cubic approximation. y = __x + (__)x2 + (__)x3 (round to six decimal places as needed.) c. (the image is attached) (round to four decimal places)

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Question: What is the slope of a least squares approximation to the following data points (1.1.2) (2.2.1) (3, 5.5). (4,8.75). (5,10.3)? Enter your answer in the space provided rounded to the hundreths place, You may use a software program to assist with the matrix math.