- 11-11.11-55: The final test and exam averages for 20 randomly selected students ...
- 11-11.11-56: The weight and systolic blood pressure of 26 randomly selected male...
- 11-11.11-57: 11-57. Consider the NFL data introduced in Exercise 11-4. (a) Estim...
- 11-11.11-58: Show that the t-statistic in Equation 11-46 for testing H0: 0 is id...
- 11-11.11-59: A random sample of 50 observations was made on the diameter of spot...
- 11-11.11-60: Suppose that a random sample of 10,000 (X, Y) pairs yielded a sampl...
- 11-11.11-61: The following data gave X the water content of snow on April 1 and ...
- 11-11.11-62: A random sample of n 25 observations was made on the time to failur...
- 11-11.11-63: Show that, for the simple linear regression model, the following st...
- 11-11.11-64: An article in the IEEE Transactions on Instrumentation and Measurem...
- 11-11.11-65: 11-65. The strength of paper used in the manufacture of cardboard b...
- 11-11.11-66: . The vapor pressure of water at various temperatures follows:
- 11-11.11-67: An electric utility is interested in developing a model relating pe...
- 11-11.11-68: Consider the following data. Suppose that the relationship between ...
- 11-11.11-69: 11-69. Consider the weight and blood pressure data in Exercise 11-5...
- 11-11.11-70: The following data, adapted from Montgomery, Peck, and Vining (2001...
- 11-11.11-71: An article in Air and Waste (Update on Ozone Trends in Californias ...
- 11-11.11-72: An article in the Journal of Applied Polymer Science (Vol. 56, pp. ...
- 11-11.11-73: Suppose that we have n pairs of observations (xi , yi ) such that t...
- 11-11.11-74: The grams of solids removed from a material ( y) is thought to be r...
- 11-11.11-75: 11-75. Two different methods can be used for measuring the temperat...
- 11-11.11-76: Consider the simple linear regression model Y 0 1x , with E() 0, V(...
- 11-11.11-77: Consider the simple linear regression model Y 0 1x , with E() 0, V(...
- 11-11.11-78: Suppose that we have assumed the straight-line regression model but...
- 11-11.11-79: Suppose that we are fitting a line and we wish to make the variance...
- 11-11.11-80: Weighted Least Squares. Suppose that we are fitting the line Y 0 1x...
- 11-11.11-81: Consider a situation where both Y and X are random variables. Let s...
- 11-11.11-82: Suppose that we are interested in fitting a simple linear regressio...
Solutions for Chapter 11-11: CORRELATION
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
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.
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.
Coeficient of determination
See R 2 .
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
The mean of the conditional probability distribution of a random variable.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The variance of the conditional probability distribution of a random variable.
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 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 .
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
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 .
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 .