- 11.3.1: Suppose that in a problem of simple linear regression, the 10 pairs...
- 11.3.2: For the data presented in Table 11.9, test at the level of signific...
- 11.3.3: For the data presented in Table 11.9, test at the level of signific...
- 11.3.4: For the data presented in Table 11.9, test at the level of signific...
- 11.3.5: For the data presented in Table 11.9, test the following hypotheses...
- 11.3.6: For the data presented in Table 11.9, test the hypothesis that when...
- 11.3.7: In a problem of simple linear regression, let D = 0 + 1x. Show that...
- 11.3.8: Let the random variable D be defined as in Exercise 7, and let the ...
- 11.3.9: For the data presented in Table 11.9, test the following hypotheses...
- 11.3.10: For the data presented in Table 11.9, construct a con- fidence inte...
- 11.3.11: For the data presented in Table 11.9, construct a con- fidence inte...
- 11.3.12: For the data presented in Table 11.9, construct a confi- dence inte...
- 11.3.13: For the data presented in Table 11.9, construct a con- fidence inte...
- 11.3.14: For the data presented in Table 11.9, construct a con- fidence inte...
- 11.3.15: Suppose that in a problem of simple linear regression, a confidence...
- 11.3.16: Let the statistic U2 be as defined by Eq. (11.3.32), and let be fix...
- 11.3.17: . For the data presented in Table 11.9, construct a con- fidence el...
- 11.3.18: a. For the data presented in Table 11.9, sketch a con- fidence band...
- 11.3.19: Determine a value of c such that in a problem of simple linear regr...
- 11.3.20: Suppose that a simple linear regression of miles per gallon (Y ) on...
- 11.3.21: Use the data in Table 11.6 on page 707. You should perform the leas...
- 11.3.22: Perform a least-squares regression of the logarithm of the 1980 fis...
- 11.3.23: Prove that the first test in Theorem 11.3.4 does indeed have level ...
- 11.3.24: Find explicit formulas (no sup or inf) for the endpoints of the int...
- 11.3.25: In this problem, we will construct a narrower con- fidence band for...
Solutions for Chapter 11.3: Linear Statistical Models
Full solutions for Probability and Statistics | 4th Edition
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
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
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
The joint probability distribution of two random variables.
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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 off-diagonal elements rij are the correlations between Xi and Xj .
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 .
Another name for factors that are arranged in a factorial experiment.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Another name for a cumulative distribution function.
In statistical quality control, that portion of a number of units or the output of a process that is defective.