- 7.2.1: Each month for several months, the average temperature in C (x) and...
- 7.2.2: In a study of the relationship between the Brinell hardness (x) and...
- 7.2.3: A least-squares line is fit to a set of points. If the total sum of...
- 7.2.4: A least-squares line is fit to a set of points. If the total sum of...
- 7.2.5: In Galtons height data (Figure 7.1, in Section 7.1), the least-squa...
- 7.2.6: In a study relating the degree of warping, in mm, of a copper plate...
- 7.2.7: Moisture content in percent by volume (x) and conductivity in mS/m ...
- 7.2.8: The following table presents shear strengths (in kN/mm) and weld di...
- 7.2.9: Structural engineers use wireless sensor networks to monitor the co...
- 7.2.10: The article Effect of Environmental Factors on Steel Plate Corrosio...
- 7.2.11: An agricultural scientist planted alfalfa on several plots of land,...
- 7.2.12: Curing times in days (x) and compressive strengths in MPa (y) were ...
- 7.2.13: Varying amounts of pectin were added to canned jellies, to study th...
- 7.2.14: An engineer wants to predict the value for y when x = 4.5, using th...
- 7.2.15: A simple random sample of 100 men aged 2534 averaged 70 inches in h...
- 7.2.16: A mixture of sucrose and water was heated on a hot plate, and the t...
Solutions for Chapter 7.2: The Least-Squares Line
Full solutions for Statistics for Engineers and Scientists | 4th Edition
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
See Arithmetic mean.
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.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
The mean of the conditional probability distribution of a random variable.
The probability of an event given that the random experiment produces an outcome in another event.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
An expression sometimes used for nonlinear regression models or polynomial regression models.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Exponential random variable
A series of tests in which changes are made to the system under study
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .