- 13.1.1: Suppose the variables x 5 commuting distance and y 5comuting time a...
- 13.1.2: The x values and standardized residuals for the chlorineflow/etch r...
- 13.1.3: Example 12.6 presented the residuals from a simple linearregression...
- 13.1.4: The accompanying data on y 5 normalized energy (Jym2)and x 5 intrao...
- 13.1.5: As the air temperature drops, river water becomes supercooledand ic...
- 13.1.6: The accompanying scatterplot is based on data providedby authors of...
- 13.1.7: Composite honeycomb sandwich panels are widelyused in various aeros...
- 13.1.8: Continuous recording of heart rate can be used to obtaininformation...
- 13.1.9: Consider the following four (x, y) data sets; the first threehave t...
- 13.1.10: a. Show that oni51 ei 5 0 when the eis are the residualsfrom a simp...
- 13.1.11: a. Express the ith residual Yi 2Yi (where Yi 5 b0 1 b1xi)in the for...
- 13.1.12: a. Could a linear regression result in residuals 23, 227,5, 17, 28,...
- 13.1.13: Recall that b0 1 b1x has a normal distribution withexpected value b...
- 13.1.14: If there is at least one x value at which more than one observation...
Solutions for Chapter 13.1: Assessing Model Adequacy
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The joint probability distribution of two random variables.
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.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
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 .
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 .
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error of estimation
The difference between an estimated value and the true value.
A subset of a sample space.
A property of a collection of events that indicates that their union equals the sample space.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Fraction defective control chart
See P chart