- 8.8.1: The Child Health and Development Studies investigate a range of top...
- 8.8.2: Exercise 8.1 introduces a data set on birth weight of babies. Anoth...
- 8.8.3: We considered the variables smoke and parity, one at a time, in mod...
- 8.8.4: Researchers interested in the relationship between absenteeism from...
- 8.8.5: A survey of 55 Duke University students asked about their GPA, numb...
- 8.8.6: Timber yield is approximately equal to the volume of a tree, howeve...
- 8.8.7: Exercise 8.3 considers a model that predicts a newborns weight usin...
- 8.8.8: Exercise 8.4 considers a model that predicts the number of days abs...
- 8.8.9: Exercise 8.3 provides regression output for the full model (includi...
- 8.8.10: Exercise 8.4 provides regression output for the full model, includi...
- 8.8.11: Suppose a social scientist is interested in studying what makes aud...
- 8.8.12: Suppose an online media streaming company is interested in building...
- 8.8.13: Exercise 8.3 presents a regression model for predicting the average...
- 8.8.14: A regression model for predicting GPA from gender and IQ was fit, a...
- 8.8.15: The common brushtail possum of the Australia region is a bit cuter ...
- 8.8.16: On January 28, 1986, a routine launch was anticipated for the Chall...
- 8.8.17: A logistic regression model was proposed for classifying common bru...
- 8.8.18: Exercise 8.16 introduced us to O-rings that were identified as a pl...
Solutions for Chapter 8: Multiple and Logistic Regression
Full solutions for OpenIntro Statistics | 3rd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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.
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.
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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.
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.
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.
Another term for the conidence coeficient.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
Formulas used to determine the number of elements in sample spaces and events.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
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
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
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 .