Where applicable, indicate who are the components of the matrix formulation of the RLM model considered.4.16. You are given the following matricescomputed for a regression analysis:9136 269136 2,114 4,176260X'X= =3,583269 4,176 8,257 7,104260 3,583 7,104 12,27645648X'y =1,2831,8219.610 0.008 -0.279 -0.044(X'X)-1)=0.008 0.509 -0.258 0.001-0.279 -0.258 0.139 0.0010.001 0.0003-0.044 0.001-1.1634610.135270= (X'X)-(X'y)=0.0199500.121954y'y = 285a. Use these results to construct the analysisof variance table.b. Give the computed regression equationand the standard errors of the regressioncoefficients.c. Compare each estimated regressioncoefficient to its standard error and use thet test to test the simple hypotheses thateach individual regression coefficient isequal to zero. State your conclusions aboutB1, B2, and B.

To begin, the given matrices represent the results of a regression analysis. The matrix \( X'X \)…

Answered: Where applicable, indicate who are the…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

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Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 2), (3, 8), (5, 10), (7, 15), (11, 24)}
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 3), (3, 6), (5, 10), (9, 18), (11, 23)} ŷ = r =
2.) The table below is about the academic performance in Mathematics of 10 students. Make a multiple regression model by following the format utilized in the above examples. AS Score (x1) MNIA Score (x2) Student Final Exam Performance Task Final Grade (y) 1 78 79 83 87VA 2 78 90 91 73 99 | 4 6 4 92 70 99 76 90 86 70 90 78 7 87 90 80 8 88 76 88 9. 84 79 86 10 80 88 89
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 3), (3, 6), (5, 12), (7, 14), (9, 18)} r =
A recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. b. What does the value 83 tell you about the relationship between hours exercisedresting heart rate?
Consider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2
The data below are the final exam scores of 10 randomly selected calculus students and the number of hours they slept the night before the exam. Compute the linear correlation coefficient, rounding to three decimal places. Hours, x Scores, y OA. 0.761 OB. 0.991 OC. 0.847 OD. 0.654 6 62 8 77 5 57 11 85 5 63 7 75 7 82 8 9 87 87 60 68
A researcher wants to investigate the influence of the average no. of nights spent per year by the tourists from Japan on the average amount spent by them. Table 3 shows the related data obtained from the Department of Statistics Malaysia website. Table 4 shows a portion of Microsoft Excel output for the regression analysis performed based on the data in Table 3. Table 3: Data on the nights spent by tourists from Japan and amount spent Year Average no. of nights spent Average amount spent (in RM billion) 2010 5.9 1.1 2011 6.1 1.1 2012 6.1 1.4 2013 6.3 1.5 2014 6.4 1.8 2015 6.1 1.6 2016 6.2 1.3 2017 6.3 1.2 2018 6.6 1.7 2019 6.9 2.3 Table 4: Regression analysis Coefficients Standard Error t Stat P-value Intercept B0 1.4555 -3.7583 0.0056 Average no. of nights spent B1 0.2312 4.7934 0.0014 a. Note that the value of B0 and B1 are missing from Table 4.…
The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year periods are shown in the table. The equation of the regression line is ModifyingAbove y=0.982x−9.080. Complete parts a and b. Money raised, x 472.2 669.3 734.5 783.9 794.4 1034.8 974.9 1202.2 Money spent, y 430.3 677.4 731.9 764.1 748.9 1023.2 942.4 1157.9 (a) Find the coefficient of determination and interpret the result. (Blank) (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? A. The coefficient of determination is the fraction of the variation in money spent that can be explained by the variation in money raised. The remaining fraction of the variation is unexplained and is due to other factors or to sampling error. B. The coefficient of determination is the fraction of the variation in money spent that is unexplained and is due to other…
The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y=47.271x+18,712.47. Issues, x Proceeds, y425 18,758468 29,602678 43,797478 31,661485 65,518396 65,33069 21,42764 11,847181 32,392157 27,561 Complete parts a and b. The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y=47.271x+18,712.47. Complete parts a and b. (a) Find the coefficient of determination and interpret the result. (Round to three decimal places as needed.) (b) Find the standard error of estimate se and interpret the result. (Round to three decimal places as needed.)
A recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. d. What percentage of variability in resting heart rate can be explained by variability inhours exercised?
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