The least squares fit line for the points (3, 3.1), (2,2.3), and (1, 2.1) has form ŷ = mx + b.First, let f be the sum of the square errors between the predicted values ŷ and y-values for the threepoints.f(m, b)=Minimize this function to find the m and b of the least square line, then write down equation of leastsquares line.y

Given: It is given that the least squares fit line for the points 3, 3.1, 2, 2.3, and 1, 2.1 has…

Answered: The least squares fit line for the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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
One of the standard curves used is harmonic decline model, that is: Q = bx/(1+ ax²) where Q is the rate of production and x is the time, b and a are the constants of the regression model. If we apply linear least squares fit for estimating b and a, what will be the value of the summation of squared errors.S Sr x, Months 11 16 18 22 90 75 65 Q, Barrels/Day 1 9 44 100 50 Sr= {(y- P(x)} 2 - (9,- #2) ²
The model, y = Bo + B₁×₁ + ß₂×2 + ε, was fitted to a sample of 33 families in order to explain household milk consumption in quarts per week, y, from the weekly income in hundreds of dollars, x₁, and the family size, x₂. The total sum of squares and regression sum of squares were found to be, SST = 162.1 and SSE(R) = 90.6. The least squares estimates of the regression parameters are bo = -0.022, b₁ = 0.051, and b₂ = 1.19. A third independent variable-number of preschool children in the household-was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.1. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not affect milk consumption. Use α=0.01. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. ''1' M P2 P3 Find the critical value. The critical value is 7.60⁰. (Round to…
For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)
The residual plot shows the residuals for the least- squares line relating price of a used car (y) to the number of miles driven (x). Residuals Residual Plot for Miles Driven vs Price 10,000 5,000 -5,000 50,000 100,000 150,000 200,000 Number of Miles Driven Based on the residual plot, is the linear model appropriate for the relationship between miles and price? No, because there are clear outliers in the residual plot. No, because there is a clear curved pattern in the residual plot. No, because there does not appear to be a pattern to the residuals. Yes, because there is a clear curved pattern in the residual plot. Yes, because there does not appear to be a pattern to the residuals.
Please ASAP
Need only handwritten solution only (not typed one).
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)
Find the least squares regression line for the points. (0, 4), (3, 2), (8, −3) y(x) = Use the regression capabilities of a graphing utility to verify your results. Use the graphing utility to plot the points and graph the regression line. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) Update Graph Student Response Graph 10 у H 1 2 3 4 5 6 7 5 Student Response Graph Description -5 8 9 X
The model, y = Bo + B₁×1 + ß₂×₂ + ε, was fitted to a sample of 33 families in order to explain household milk consumption in quarts per week, y, from the weekly income in hundreds of dollars, X₁, and the family size, x2. The total sum of squares and regression sum of squares were found to be, SST = 162.1 and SSE(R) = 90.6. The least squares estimates of the regression parameters are bo = -0.022, b₁ = 0.051, and b₂ = 1.19. A third independent variable number of preschool children in the household-was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.1. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not affect milk consumption. Use α = 0.01. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternative hypotheses below. A. Ho: B3 = 0 |…
A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) Efficiency (%) 0 25 50 75 100 | 60 70 75 81 84 (a) Obtain the least squares fit of a straight line to the amount of lubricating oil. (b) Test whether or not the slope B, = 0. Take a = 0.05 as your level of significance. (c) Construct a 90% confidence interval on the mean response at xo = 10 ml.
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.

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