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FSU - HIST - AMH 2097
Summary, by late 1700sNew groups form over long processesCreeks, Choctaws, Cherokees, ChickasawsTrade involves Indians in international economy, cultural changes and increased conflict Slaving then deerskins Hunting v. FarmingIncreased contact with
FSU - HIST - AMH
Timucua-largest ~ 200,000 people not one unified tribe meeting squares not mounds not a strict political structure- confederacy status predecessors to many tribesCulture - Sun and moon gods & deer and bear - Did not hunt constantly- smaller animals and
FSU - HIST - AMH
Ballgame -Timucua Ballgame adapted from Le Moyne Large groups of people, sometimes entire villages Ball pole in the center of the town (highlight the town) Celebrities on par with the leaders Fufills religious reasons- pleases sun, thunder, and rain gods
National University of Singapore - STAT - ST3131
Solutions to Tutorial Questions 1 1.For model Yi = 0 + 1 Xi + iassume that X = 0 is within the scope of the model. What is the implication for the regression function Yi = 0 + 1 Xi if 0 = 0 so that the model is Yi = 1 Xi + i ? How would the regression f
National University of Singapore - STAT - ST3131
Solutions to Tutorial 2 1. (a) Y = 10.2 + 4.00X (SE ) (0.6633) (0.4690) M SE = 2.199289, see code (R code) for the plot. Yes, the linear regression function ts the data well. (b) Y = 10.2 + 4.00 1 = 14.2 (c) b1 t(0.975, 8) s(b1 ) = 4 2.306 0.469 = [2.9184
National University of Singapore - STAT - ST3131
Solution to TUTORIAL 3 1. (R code) (a) [3.061384, 3.341033] on average, with 95% condence, the mean freshman GPA is between 3.061384 and 3.341033 when their ACT test scores are 28 (b) [1.959355, 4.443063], with 95% condence her GPA will be between 1.95935
National University of Singapore - STAT - ST3131
Solutions to Tutorial 4 1. An output of a simple linear regression model Yi = 0 + 1 Xi + i , is as follows Coecients: Estimate Std. Error t value P-value (Intercept) -0.07727 0.12005 -0.644 0.537814 x 0.97295 0.14345 6.783 0.000140 Residual standard error
National University of Singapore - STAT - ST3131
Tutorial 5 1. Suppose we have n = 10 observations (Xi , Yi ) and t the data with modelYi = 0 + 1 Xi + i with i , i = 1, ., 10 are IID N (0, 2 ). We have the following calculations.n X = 0.5669,n i=1 Y = 0.9624,i=1 nYi2 = 10.2695,Xi2= 4.0169,i=1
National University of Singapore - STAT - ST3131
Solution to Tutorial 6 1.For each of the following regression models, indicate whether it is a general linear regression model. If not, state whether it can be expressed in the form of a linear regression model after some suitable transformation a. b. c.
National University of Singapore - STAT - ST3131
Tutorial 7 1.A student stated: Adding predictor variables to a regression model can never reduce R2 , so we should include all available predictor variables in the model. Comment.Bigger R2 , means the tting is better. Better tting does not imply better
National University of Singapore - STAT - ST3131
Solution to Tutorial 8 1. (a) Hard hat: E (Y ) = 0 + 2 + 1 X1 Bump hat: E (Y ) = 0 + 3 + 1 X1 None: E (Y ) = 0 + 1 X1 (b) (1) H0 : 3 = 0; Ha : 3 = 0; (1) H0 : 3 = 2 ; Ha : 3 = 2 ; 2. (1) 3 means the dierence in the intercepts between M2 and M4 (2) 4 3 is
National University of Singapore - STAT - ST3131
Solutions to Tutorial 9 1. (a) (145) (b) (0)0.9596; (4)0.7338; (45)(-0.1927); (145)(-4.6600) The model calculated: (0), (1), (2), (3), (4), (5), (14), (24), (34), (45), (145), (245), (345), (1245), (1345). (c) (12345)(-4.5600), (1345)(-4.6157), (145)(-4.6
National University of Singapore - STAT - ST3131
Tutorial 10 1. Derive the weighted least square normal equations for tting a simple linear regression func2 tion when i = kXi , where k > 0 is a constant.Let Qw (b0 , b1 ) =n i=11 (Yi b0 b1 Xi )2 kXiand Qw (b0 , b1 ) = 2 b0nQw (b0 , b1 ) = 2 b1i=1
National University of Singapore - STAT - ST3131
Tutorial Questions 1 1. For model Yi = 0 + 1 Xi + i assume that X = 0 is within the scope of the model. What is the implication for the regression function Yi = 0 + 1 Xi if 0 = 0 so that the model is Yi = 1 Xi + i ? How would the regression function Yi =
National University of Singapore - STAT - ST3131
Tutorial 2 1. Airfreight breakage A substance used in biological and medical research is shipped by airfreight to users in cartons of 1000 ampules. In the (data), X is the number of times the carton was transferred from one aircraft to another over the sh
National University of Singapore - STAT - ST3131
TUTORIAL 3 1. Refer to the Grade point average problem (see tutorial 1) (a) obtain a 95% percent interval estimate of the mean freshman GPA for students whose ACT test score is 28. Interpret your condence interval. (b) Mary Jones obtained a score of 28 on
National University of Singapore - STAT - ST3131
Tutorial 4 1. An output of a simple linear regression model Yi = 0 + 1 Xi + i , is as follows Coecients: Estimate Std. Error t value P-value (Intercept) -0.07727 0.12005 -0.644 0.537814 x 0.97295 0.14345 6.783 0.000140 Residual standard error: 0.3761 on 8
National University of Singapore - STAT - ST3131
Tutorial 5 1. Suppose we have n = 10 observations (Xi , Yi ) and t the data with model Yi = 0 + 1 Xi + i with i , i = 1, ., 10 are IID N (0, 2 ). We have the following calculations.n X = 0.5669,n i=1 Y = 0.9624,i=1 nYi2 = 10.2695,Xi2 = 4.0169,Xi Y
National University of Singapore - STAT - ST3131
Tutorial 6 1. For each of the following regression models, indicate whether it is a general linear regression model. If not, state whether it can be expressed in the form of a linear regression model after some suitable transformation a. b. c. d. e. Yi =
National University of Singapore - STAT - ST3131
Tutorial 7 1. A student stated: Adding predictor variables to a regression model can never reduce R2 , so we should include all available predictor variables in the model. Comment. 2. For a model with X1 , X2 , X3 , X4 predictors, we have n = 30 and SSE (
National University of Singapore - STAT - ST3131
Tutorial 8 1. In regression analysis of on-the-job head injuries of warehouse laborers caused by falling objects. Y is a measure of severity of the injury, X1 is an index reecting both the weight of the object and the distance it fell, and D1 and D2 are i
National University of Singapore - STAT - ST3131
Tutorial 9 1. Suppose Y has 5 covariates X1 , X2 , X3 , X4 , X5 denote any model Y = 0 + i Xi + j Xj + k Xk + by (ijk). All the models can be listed as (0), (1), (2), (3), (4), (5), (12), (13), (14), (15), (23), (24), (25), (34), (35), (45), (123), (124),
National University of Singapore - STAT - ST3131
Tutorial 10 1. Derive the weighted least square normal equations for tting a simple linear regression2 function when i = kXi , where k > 0 is a constant.2. For linear regression model Yi = 0 + 1 Xi1 + . + p Xip + i , with 2 1i = 1, ., n. 0 . 0 1 0 2
National University of Singapore - STAT - ST4240
Midterm Test for ST4240 Data Mining (please answer all the questions for full marks. Please send your answer to staxyc@nus.edu.sg)1. For data A (at http:/www.stat.nus.edu.sg/~staxyc/DM07testdata1.dat), there are 5 predictors X1, , X5 and response Y. A Si
National University of Singapore - STAT - ST4240
Tutorial 1 1. Prove the solution of ridge regression estimatorn p R = mincfw_ i=1 n(Yi Xi )2 + k=1 n2 kis R = (Xi Xi + I )i=11 i=1Xi Yior R = (X X + I )1 X Y . what about R = mincfw_ i=1 n p(Yi Xi ) +k=122 k kwhere k > 0, k = 1, ., p 2.
National University of Singapore - STAT - ST4240
Tutorial 1 1.Prove the solution of ridge regression estimatorn p R = mincfw_( Yi Xi ) + k=12k2i=1is R = (nXi Xi + I )i=11nXi Yii=1or1 R = (X X + I ) X Y.what about R = mincfw_np( Yi Xi ) +k=12k k2i=1where k > 0, k = 1, ., p2.
National University of Singapore - STAT - ST4240
Tutorial 2 1. Suppose we have observations (Xi , Yi ) sorted according to X : ., (0.5, 1.2), (0.6, 1.4), (0.7, 1.5), (0.8, 1.7), (0.9, 1.5), (1.0, 2), (1.1, 2.2), (1.2, 1.6), (1.3, 1.7), (1.4, 1.9), (1.5, 1.7), . If we use Epanechnikov kernel with bandwid
National University of Singapore - STAT - ST4240
Tutorial 2: suggested solution 1.Suppose we have observations (Xi , Yi ) sorted according to X : ., (0.5, 1.2), (0.6, 1.4), (0.7, 1.5), (0.8, 1.7), (0.9, 1.5), (1.0, 2), (1.1, 2.2), (1.2, 1.6), (1.3, 1.7), (1.4, 1.9), (1.5, 1.7), . If we use Epanechnikov
National University of Singapore - STAT - ST4240
Tutorial 3 1. Suppose that X follows a uniform distribution, then for the inner points, the local linear kernel estimator and local constant (NW) estimator have the same asymptotic MSE. 2. For model Y = sin(2X ) + where X unif orm(0, 1) and is independent
National University of Singapore - STAT - ST4240
Suggested Solutions for Tutorial 3 1.Suppose that X follows a uniform distribution, then for the inner points, the local linear kernel estimator and local constant (NW) estimator have the same asymptotic MSE.The MSE for NW kernel estimator is 1 2 d0 M S
National University of Singapore - STAT - ST4240
Tutorial 4 1. The air pollutants include nitrogen dioxide (NO2 ), Carbon dioxide (CO), sulphur dioxide (SO2 ), respirable particulates (PM), Ozone (O3 ) and others. Pollutants can be classied as either primary or secondary. Primary pollutants are substanc
National University of Singapore - STAT - ST4240
Tutorial 3: Suggested solutions 1.The air pollutants include nitrogen dioxide (NO2 ), Carbon dioxide (CO), sulphur dioxide (SO2 ), respirable particulates (PM), Ozone (O3 ) and others. Pollutants can be classied as either primary or secondary. Primary po
National University of Singapore - STAT - ST4240
Tutorial 5 1. comparing the estimators of on the top of page 2 (chapter 2 part 1 ) and (2.3) on page 3 of part 2. Explain why there is no weight function in the estimator of page 2. 2. Based on the notation in Lecture note (Chapter 2, part 2), eqns betwee
National University of Singapore - STAT - ST4240
Tutorial 4: Suggested solutions 1.comparing the estimators on the top of page 4 (chapter 2 part 1 ) and (2.3) on page 3 of part 2. Explain why there is not weight function in the estimator of page 4.Because the estimation on the top of page 2 (chapter 2
National University of Singapore - STAT - ST4240
Tutorial 6 1. Suppose m(x1 , ., xp ) = (1 x1 + . + p xp ). Prove that m(x1 ,.,xp ) x1 m(x1 ,.,xp ) x2 xp 1 = (1 x1 + . + p xp ) 2 . . m(x1 ,.,xp ) p 2. For a single-index model Y = ( X ) + . Suppose (Xi , yi ) are the observations and the estimator for
National University of Singapore - STAT - ST4240
Tutorial 6: suggested solutions 1.Suppose m(x1 , ., xp ) = (1 x1 + . + p xp ). Prove that m(x ,.,xp ) 1 x1 1 m(x1 ,.,xp ) 2 x2 = (1 x1 + . + p xp ) . . m(x1 ,.,xp ) xp pproof: Because m(x1 , ., xp ) = (1 x1 + . + p xp )k xk 2.For a single-index model
National University of Singapore - STAT - ST4240
Tutorial 7 1. Suppose we use model Y= a0 + b0 x1 + c0 x2 + 0 , if x1 + x2 < 0, a1 + b1 x1 + c1 x2 + 1 , if x1 + x2 0.to t data (xi1 , xi2 , Yi ), i = 1, 2, ., n. Write the procedure to calculate the (deleteone-out) CV value. 2. For model Y = 4x1 x2 + , n
National University of Singapore - STAT - ST4240
Tutorial 6: suggested solutions 1.Suppose we use model Y= a0 + b0 x1 + c0 x2 + 0 , a1 + b1 x1 + c1 x2 + 1 , if x1 + x2 < 0, if x1 + x2 0.to t data (xi1 , xi2 , Yi ), i = 1, 2, ., n. Write the procedure to calculate the (delete-one-out) CV value.CV= n
National University of Singapore - STAT - ST4240
Tutorial 8 1. suppose we have sample (xi , yi ), i = 1, ., n. we estimate the regression model yi = g (xi ) + i , where g (x) is a spline function of the formJ +4g (x) =j =1j Bj (x)(a) Estimate the derivative g (x) of g (x) (b) nd the 95% condence ba
National University of Singapore - STAT - ST4240
Tutorial 8: suggested solutions 1.suppose we have sample (xi , yi ), i = 1, ., n. we estimate the regression model yi = g (xi ) + i , where g (x) is a spline function of the formJ +4g (x) =j =1j Bj (x)(a) Estimate the derivative g (x) of g (x) (b) n
National University of Singapore - STAT - ST4240
Tutorial 9 1. Suppose we need to estimate a varying coecient model Y = a0 (x1 ) + a1 (x2 )x3 + with sample (xi1 , ., xi3 , Yi ), i = 1, ., n. Using cubic spline to approximate ak (z ). (a) write the expression for the estimator of a1 (z ) (b) nd the 95% c
National University of Singapore - STAT - ST4240
Tutorial 9: solutions 1.Suppose we need to estimate a varying coecient model Y = a0 (x1 ) + a1 (x2 )x3 + with sample (xi1 , ., xi3 , Yi ), i = 1, ., n. Using cubic spline to approximate ak (z ). (a) write the expression for the estimator of a1 (z ) (b) n
National University of Singapore - STAT - ST4240
Tutorial 10 1. Both linear regression model and separating hyperplane in classication (in e.g. SVM) are looking for a linear combination of covariates. Explain their dierence in the estimation and the rules in prediction. 2. we can use support vector mach
National University of Singapore - STAT - ST4240
Tutorial 10: solutions 1.Both linear regression model and separating hyperplane in classication (in e.g. SVM) are looking for a linear combination ofcovariates. Explain their dierence in the estimation and the rules in prediction.Linear regression mode
National University of Singapore - STAT - ST4240
Tutorial 11 1. Based on (training set), using all the classication methods to classify the (validation set). Please adjust the parameters in all the method to rene the performance of the methods for the validation set.1
National University of Singapore - STAT - ST4240
Tutorial 11: solutions 1. Based on (training set), using all the classication methods to classify the (validation set). Please adjust the parameters in all the method to rene the performance of the methods for the validation set.(CODE)1
Abant İzzet Baysal University - ENGLISH - 23
A dvantages Cloud base- T his service provides companies the opportunity to have a cloud based platform. For instance, the maintenance of cloud computing applications is easier, since they do not have to be installed on each persons computer. In addition,
University of Phoenix - MAT - 116
Axia College MaterialAppendix D Landscape DesignLandscape designers often use coordinate geometry and algebra as they help their clients. In many regions, landscape design is a growing field. With the increasing popularity of do-it-yourself television s
Washington - CHEM - 145
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Washington - CHEM - 145
Balancing Chemical Equations I. Chemical Equations A. Reactants written on left B. Products written on right C. Conditions are written over/under the arrow D. Atoms and masses are conserved in chem. rxn 1. meaning you must have equal masses on each side o
Washington - CHEM - 145
Name_Calculating empirical formulas of compoundsExample:What would be the empirical formula for a compound that contains 32.38% Na, 22.65% S, and 44.99% O 1. Assume you have 100grams. So convert the percentages to grams2. Convert from grams to moles by
Washington - CHEM - 145
C alorimetry WorksheetsPhase ChangesImagine a simplified model of a solid as tiny particles bonded together by springs. The spring represent the electromagnetic forces between the particles. If the thermal energy of a solid is increased, both the potent
Washington - CHEM - 145
Study Guide Chapter 1-3, and portions of 15 & 17 Key WordsHomogeneous/heterogeneous Density Mixture Compound Elements Solution/solvent/solute Matter/atoms/Molecules Calorimetry Heat/Temperature/specific heat/heat capacity Know the symbols Q, Cp, : if Q i
Washington - CHEM - 145
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Washington - CHEM - 145
Dalton's Law of Partial Pressures Page 334-6 John Dalton was the first to form a hypothesis about the pressure one gas exerts on another in a mixture. When a gas is one of a mixture, its pressure is called a partial pressure. After experimenting with gase
Washington - CHEM - 145
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Name:Gas law problems1. A sample of gas occupies 14.3 L at 19 C and 1.2 atm. How many moles of gas are present?2. How many moles of Hydrogen gas are present in a 50 L cylinder if the pressure is 10 atm and the temp is 27 C? R=.082 liter-atm/mol-K3. Wh