 14.1: Convert the following relationships into linear relationships by ma...
 14.2: Plot y versus x for the following pairs: x .34 1.38 .65 .68 1.40 .8...
 14.3: Suppose that yi = + ei , where i = 1, . . . , n and the ei are inde...
 14.4: Consider a standard linear regression model in which the freshman G...
 14.5: Three objects are located on a line at points p1 < p2 < p3. These l...
 14.6: Two objects of unknown weights w1 and w2 are weighed on an errorpr...
 14.7: (Weighted Least Squares) Suppose that in the model yi =0 +1xi +ei ,...
 14.8: (The QR Method) This problem outlines the basic ideas of an alterna...
 14.9: (Cholesky Decomposition) This problem outlines the basic ideas of a...
 14.10: Show that the least squares estimates of the slope and intercept of...
 14.11: Show that if x = 0, the estimated slope and intercept are uncorrela...
 14.12: Use the result of to show that the line fit by the method of least ...
 14.13: Suppose that a line is fit by the method of least squares to n poin...
 14.14: dealt with howto form a confidence interval for the value of a line...
 14.15: Find the least squares estimate of for fitting the line y = x to po...
 14.16: Consider fitting the curve y = 0x+1x2 to points (xi , yi ), where i...
 14.17: This problem extends some of the material in Section 14.2.3. Let X ...
 14.18: Suppose that Yi = 0 + 1xi + ei , i = 1, . . . , n where the ei are ...
 14.19: a. Show that the vector of residuals is orthogonal to every column ...
 14.20: Assume that the columns of X, X1, . . . , Xp, are orthogonal; that ...
 14.21: Suppose that n points x1, . . . , xn are to be placed in the interv...
 14.22: Suppose that the relation of family income to consumption is linear...
 14.23: Suppose that grades on a midterm and a final have a correlation coe...
 14.24: Suppose that the independent variables in a least squares problem a...
 14.25: Suppose that each setting xi of the independent variables in a simp...
 14.26: Suppose that Z1, Z2, Z3, Z4 are random variables with Var(Zi ) = 1 ...
 14.27: For the standard linear model of Section 14.4.2, show that 2 I = _Y...
 14.28: Suppose that X1, . . . , Xn are independent with mean i and common ...
 14.29: Assume that X1 and X2 are uncorrelated random variables with varian...
 14.30: Let X1, . . . , Xn be random variables with Var(Xi ) = 2 and Cov(Xi...
 14.31: Let Z be a random vector with 4 components and covariance matrix 2 ...
 14.32: Let X be a random nvector and let Y be a random vector with Y1 = X...
 14.33: a. Let X N(0, 1) and E N(0, 1) be independent, and let Y = X + E. S...
 14.34: Generate a bivariate sample of size 50 as in with correlation coeff...
 14.35: An investigatorwants to use multiple regression to predict a variab...
 14.36: The file bismuth contains the transition pressure (bar) of the bism...
 14.37: Dissociation pressure for a reaction involving barium nitride was r...
 14.38: The file sapphire lists observed values of Youngs modulus (g) measu...
 14.39: As part of a nuclear safeguards program, the contents of a tank are...
 14.40: The following data come from the calibration of a proving ring, a d...
 14.41: The file chestnut contains the diameter (feet) at breast height (DB...
 14.42: The stopping distance (y) of an automobile on a certain road was st...
 14.43: Chang (1945) studied the rate of sedimentation of amoebic cysts in ...
 14.44: Cogswell (1973) studied a method of measuring resistance to breathi...
 14.45: The file reading contains average reading scores of thirdgraders f...
 14.46: Measurement of the concentration of small asbestos fibers is import...
 14.47: Aerial survey methods are used to estimate the number of snow geese...
 14.48: The volume, height, and diameter at 4.5 ft above ground level were ...
 14.49: The file flowocc contains data collected by loop detectors in all ...
 14.50: The file binary59683 contains measurements of the light of an astro...
 14.51: The following table shows the monthly returns of stock in Disney, M...
 14.52: The file bodytemp contains normal body temperature readings (degree...
 14.53: Old Faithful geyser in Yellowstone National Park, Wyoming, derives ...
 14.54: In 1970, Congress instituted a lottery for the military draft to su...
 14.55: When gasoline is pumped into the tank of an automobile, hydrocarbon...
 14.56: Recordings of the levels of pollutants and various meteorological c...
Solutions for Chapter 14: Linear Least Squares
Full solutions for Mathematical Statistics and Data Analysis  3rd Edition
ISBN: 9788131519547
Solutions for Chapter 14: Linear Least Squares
Get Full SolutionsMathematical Statistics and Data Analysis was written by and is associated to the ISBN: 9788131519547. Since 56 problems in chapter 14: Linear Least Squares have been answered, more than 15268 students have viewed full stepbystep solutions from this chapter. Chapter 14: Linear Least Squares includes 56 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Statistics and Data Analysis, edition: 3.

Acceptance region
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Bayes’ estimator
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Bimodal distribution.
A distribution with two modes

Bivariate distribution
The joint probability distribution of two random variables.

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Conidence level
Another term for the conidence coeficient.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Fisher’s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials