Question

1. The volume, height, and diameter at 4.5 ft sbove ground level were measured for a sample of 5 black berry trecs. The data are shown in the table below. Answer the following questi ions using hand calculations only lume (y 16.4 21.3 34.5 55.4 72 69 78 81 8.3 10.5 11.7 14.0 17.3 (a) Develop a multiple lincar regression model of Volume on Height and Diameter. (b) Write out the MLR model using the matrix notations. Explicitly spocify all matrices and vectors used in the model (c) Specify the dimensions of all matrices/vectors in the model (d) Write the least-squares normal equations in mstrix form. (e) What is the least-squares estimator of β. You don't have to do the matrix inversion, just leave it there. (f) Given that 2.5552-0.6387 10.7504.7154-1.8408 0.0006 0.0231-0.1813 0.0784 0.0132 0.1759-0.0705 0.232.0718 0.0862 (X,X)-1X' find the least squares estimator β (g) Find the estimated volumes for these 5 troes. (h) Find all residuals (i) What is the estimated value of σ2? G) Test for significsnce of regression. (k) Test H0 : β1 : 0 versus Ha : β1 You need 148.12632.5284 3.1697 X'X)-2.5284 0.044180.05993 3.1697 0.05993 0.1024 (1) Test Ho : β2 0 versus Ha : A 0. (m) Give a 95% confidence interval for (n) Give a 99% confidence interval for (o) Give a 95% confidence interval for A-

Answer 1

0 I Solution ression sis Volume (y) Vensus H osme Vasuon CA SiS Source DF Ad SS AM value P-valuse emession2 1262-o63u 550 ols imeten18 16 7164 15 650 058 Exror Tobol 2 22-16 11-38 12S4.87 Model Summas 3.37459 9g. 237 96.45% 36-1 %

2. Co-elficients Team Coe^ SE Co Constant -2-s 41 6 0-220 Height (x) 0 639 0-104 63 4.86 0.709 ο.qo ression b, rt he MR modd usng Be. máai:t notationsl setyl mabices nd vectorsuSed n He mode! the Muliple ea Regqession is The least gu des estontorofß iso-639

A, find the estimated. Vusesse 5 brees. The estimatedume o tese trees is FITS 168593 3589 21. 56 7 3 136 53 148+2 Findall vesiduals the esidnals oe SaSe REST 2.614064 1589? 0261 2.639 16 2 5146 e, dat is the estinated value of e's the estinated. vabe f vsiance is(3ns e esima 11.3a

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