6.27. In a small-scale regression study, the following data were obtained:i:23456Xn:X12:Y;:741632184133337495314275289155Assume that regression model (6.1) with independent normal error terms is appropriate. Usingmatrix methods, obtain (a) b; (b) e; (c) H; (d) SSR; (e) s² {b}; (f ) Ýn when Xp1 = 10, X42 = 30;(g) s²{Ýn} when Xµ1 = 10, Xp2 = 30.

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Answered: 6.27. In a small-scale regression…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The following table shows the original marks of six candidates in two examinations. Candidate A B C D E F English 38 62 56 42 59 48 History 64 84 84 60 73 69 (c) Determine the regression line in the form y = a + bx (d) Using your equation found in (c), predict the History mark of a candidate scoring 50 in English.
Consider the data. X;| 1 2 3 4 5 y, 4 8 11 12 The estimated regression equation for these data is ý = 2.30 + 1.90x. (a) Compute SSE, SST, and SSR using equations SSE = E(y; - 9)?, SST = E(y; - y)?, and SSR = E(ŷ; - y)?. SSE = SST = SSR = (b) Compute the coefficient of determination r2. r2 Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line. O The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. O The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. (c) Compute the sample…
Consider the data. xi 3 12 6 20 14 yi 55 35 60 15 25 The estimated regression equation for these data is ŷ = 68.25 − 2.75x. (a) Compute SSE, SST, and SSR using equations SSE = Σ(yi − ŷi)2, SST = Σ(yi − y)2, and SSR = Σ(ŷi − y)2. SSE=SST=SSR= (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line. The least squares line provided a good fit as a large proportion of the variability in y has…
The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained. Systolic Blood pressuex1 Age (years)x2 Weight (pounds)x3 132 52 173 143 59 184 153 67 194 162 73 211 154 64 196 168 74 220 137 54 188 149 61 188 159 65 207 128 46 167 166 72 217 a) Look at the coefficients of the regression equation. Write out the regression equation. (Use 3 decimal places.) x1 = _____ + _____ x2 + ____x3 b) If age were held fixed, but a person put on 10 pounds, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)c) If a person kept the same weight but got 10 years older, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)
The number of speeding tickets issued (Y) and the number of radar traps set up by police officials on an expressway (X) during nine weekends are shown below: No. of speed traps X: 10 12 15 8 8 12 11 7 13 14 No. of speeding tickets issued Y: 76 84 93 61 79 70 55 84 85 (a) Draw a scatter plot of the data. (b) Find the equation of the least squares regression line using the information below: x, -102, Σx-1212, Σν- 687, Σν,-53649, ΣΧ.y, 8036. (Show the details of your work.) T
A statistical program is recommended. A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is ý = 82 + 4x. Years of Annual Sales Salesperson Experience ($1,000s) 1 80 2 97 3 4 97 4 4 107 5 6 103 6 8 116 7 10 119 8 10 118 9 11 127 10 13 136 (a) Compute the residuals. Years of Experience Annual Sales ($1,000s) Residuals 1 80 3 97 4 97 4 107 6 103 8 116 10 119 10 118 11 127 13 136 Construct a residual plot.

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