Statitics Questions:-
A research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number (r ) 2.1 4.31 84 22.11 5.1 11:40 14.5 24.15 44 6.21 62 5.65 12.5 9.71 7.0 12.00 17.2 14.25 7.1 8.63 Find the model specification matrix for the modelA research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number 2.1 4.31 84 22.11 5.1 11:40 14.5 24.15 4.4 6.21 6.2 5.65 12.5 9.71 7.0 12.00 17.2 14.25 7.1 8.63 For the model of Exercise 44, 529839 - 02535552 -.0182053 (XX)= -.0253552 00772376 -.00337026 -.0182053 .00337026 003942239 60 X'y = 604.2 860.52 $1 = .94334776 Use this information to estimate the model.A research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number (V) 2.1 4.31 84 22.11 5.1 11:40 14.5 24.15 44 6.21 62 5.65 125 9.71 7.0 12.00 17.2 14.25 7.1 8.63 Find R for the estimated model of Exercise 45.A research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number (F) 2,1 4.31 22.11 5.1 11:40 14.5 24.15 44 6.21 UNDWWELIN 62 5.65 125 9.71 7.0 12.00 17.2 14.25 7.1 8.63 Estimate o, the correlation between the observed and predicted responses for the model of Exercise 45.A research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number (F) (r, ) 21 4.31 84 22.11 5.1 11:40 14.5 24.15 4 4 6.21 62 5.65 12.5 9.71 T.0 12.00 17.2 14.25 7.1 8.63 Test for significant regression for the curve estimated in Exercise 45.A research study was conducted on cracking of latex paint on wooden structures. The primary concern in the study is to investigate the effect of water permeability and fracture energy (energy to propagate a crack through paint film) on paint crack rating. The investigation yielded the following data: Sample Crack rating Permeability Fracture energy number (F) (r,) 2.1 4.31 22.11 5.1 11:40 14.5 24.15 44 6.21 30 0DAWN 6.2 5.65 125 9.71 7.0 12.00 17.2 14.25 7.1 8.63 Test Ho: By = 0. Do you think that x, is needed in a model that already contains the variable x. ? Explain.Consider the model = Bot Bix + Brixi + B2x2 Express this model in the general linear form of (12.1).In Exercise 3 we considered the model Anna = Bo + Box, + Box; based on these data: 00 10 (a) Find the model specification matrix. (b) Find XX. (c) Find Xy. (d) Find the normal equations, and compare them to those found in Exercise 3. (e) Show that 1680 -4 -200 16 16 16 (XX)= -4 2 0 16 16 -200 0 24 16 16 9 (f) Verify that h = -5 0In simple linear regression, j}, the estimated response for a given value of x can be written in matrix notation as follows: 3r= [ha is] [i] {a} 'v'erifv that the above technique is valid. rs} Use this method and the results of Exercise 7" to estimate the ave rage energy.r consumed by a household for which the inoome is $5D,_ to} Use this method and the results of Exercise 8 to estimate the pitch of a particular oonnector of length .133 inch. {d} Use this method and the results of Exercise 3 to estimate the surface feet per minute that can be covered when a wheel is used at 3450 rpm {revolutions per minute}. In developing a simple linear regression model for predicting gasoline mileage, based on the weight of the car, these data are available: 1.35 1.90 1.70 1.80 1.30 2.05 1.60 1.80 1.85 1.40 17.9 16.5 16.4 16.8 18.8 15.5 17.5 16.4 15.9 18.3 (a) Find the model specification matrix. (b) Find XX. (c) Find Xy. () Find the normal equations via matrix algebra. (e) Find (XX)-1. (f) Find the least-squares estimates for Bo and B, by using matrix algebra. Compare these to the values found in Example 11.3.3. Example 11.3.3. An investigation is conducted to study gasoline mileage in auto- mobiles when used exclusively for urban driving. Ten properly tuned and serviced automobiles manufactured during the same year are used in the study. Each automo- bile is driven for 1000 miles, and the average number of miles per gallon (mi/gal) ob- tained (Y) and the weight of the car in tons (X) are recorded. These data result: Car number 10 Miles per gallon (y) 17.9 16.5 16.4 16.8 13.8 15.5 17.5 16.4 15.9 18.3 Weight in tons (x) 1.35 1.90 1.70 1.80 1.30 2.05 1.60 1.80 1.85 1.40 Summary statistics for these data are n = 10 Ex2 = 28.6375 Ey? = 2900.46 S. = 581 Spy = -2.345 Ex = 16.75 Ey = 170.0 Exy = 282.405 Spy = 10.46 B1 =b = nExy - ExEy nEx - (Ex) 10(282.405) - (16.75) (170.0) 10(28.6375) - (16.75) = -4.03 Bo = bo = y-b,i = 17.0 - (-4.03) (1.675) =23.75 The estimated line of regression is Myix = bo + bix = 23.75 - 4.03x The reader can verify that Ho: B, = 0 can be rejected with P
