- 12.7.39: Refer to Exercise 12.6.a. Estimate the average value of y when x 1,...
- 12.7.40: Refer to Exercise 12.7. Portions of theMINITAB printout are shown h...
- 12.7.41: What to Buy? A marketing researchexperiment was conducted to study ...
- 12.7.42: Housing Prices The data in the tablegive the square footages and sa...
- 12.7.43: Housing Prices II Refer to Exercise 12.42and data set EX1242.a. Est...
- 12.7.44: Strawberries III The following data (Exercises12.18 and 12.27) were...
- 12.7.45: Drew Brees The number of passescompleted and the total number of pa...
- 12.7.46: Drew Brees, continued Refer to Exercise12.45.a. Estimate the averag...
Solutions for Chapter 12.7: Estimation and Prediction Using the Fitted Line
Full solutions for Introduction to Probability and Statistics 1 | 14th Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
Another name for factors that are arranged in a factorial experiment.
An expression sometimes used for nonlinear regression models or polynomial regression models.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A probability distribution for a discrete random variable
A subset of a sample space.
Exponential random variable
A series of tests in which changes are made to the system under study
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .