- 12.5.19: Refer to Exercise 12.6. The data are reproducedbelow.x 2 10 1 2y 1 ...
- 12.5.20: Refer to Exercise 12.19. Find a 95% confi-dence interval for the sl...
- 12.5.21: Refer to Exercise 12.7. The data, along withthe MINITAB analysis of...
- 12.5.22: Refer to Exercise 12.8. The data, along withthe MS Excel analysis o...
- 12.5.23: Chirping Crickets In Exercise 3.18,we found that male crickets chir...
- 12.5.24: Gestation Times and Longevity Thetable below, a subset of the data ...
- 12.5.25: Professor Asimov, continued Refer to thedata in Exercise 12.9, rela...
- 12.5.26: Refer to the sleep deprivation experimentdescribed in Exercises 12....
- 12.5.27: Strawberries II The following data (Exercise12.18 and data set EX12...
- 12.5.28: Laptops and Learning In Exercise1.61 we described an informal exper...
- 12.5.29: Laptops and Learning, continued Refer toExercise 12.28.a. Use the M...
- 12.5.30: Armspan and Height II In Exercise 12.17(data set EX1217), we measur...
Solutions for Chapter 12.5: Testing the Usefulness of the Linear Regression Model
Full solutions for Introduction to Probability and Statistics 1 | 14th Edition
Solutions for Chapter 12.5: Testing the Usefulness of the Linear Regression ModelGet Full Solutions
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
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
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.
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
A matrix that provides the tests that are to be conducted in an experiment.
A study in which a sample from a population is used to make inference to the population. See Analytic study
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.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.