- 10-3.1: What is meant by the explained variation? How is it computed? Expla...
- 10-3.2: What is meant by the unexplained variation? How is it computed? Une...
- 10-3.3: What is meant by the total variation? How is it computed?
- 10-3.4: Define the coefficient of determination.
- 10-3.5: How is the coefficient of determination found?
- 10-3.6: Define the coefficient of nondetermination. It is the percent of th...
- 10-3.7: How is the coefficient of nondetermination found? The coefficient o...
- 10-3.8: For Exercises 8 through 13, find the coefficients of determination ...
- 10-3.9: For Exercises 8 through 13, find the coefficients of determination ...
- 10-3.10: For Exercises 8 through 13, find the coefficients of determination ...
- 10-3.11: For Exercises 8 through 13, find the coefficients of determination ...
- 10-3.12: For Exercises 8 through 13, find the coefficients of determination ...
- 10-3.13: For Exercises 8 through 13, find the coefficients of determination ...
- 10-3.14: Define the standard error of the estimate for regression. When can ...
- 10-3.15: Compute the standard error of the estimate for Exercise 13 in Secti...
- 10-3.16: Compute the standard error of the estimate for Exercise 14 in Secti...
- 10-3.17: Compute the standard error of the estimate for Exercise 15 in Secti...
- 10-3.18: Compute the standard error of the estimate for Exercise 16 in Secti...
- 10-3.19: For the data in Exercises 13 in Sections 101 and 102 and 15 in Sect...
- 10-3.20: For the data in Exercises 14 in Sections 101 and 102 and 16 in Sect...
- 10-3.21: For the data in Exercises 15 in Sections 101 and 102 and 17 in Sect...
- 10-3.22: For the data in Exercises 16 in Sections 101 and 102 and 18 in Sect...
Solutions for Chapter 10-3: Coefficient of Determination and Standard Error of the Estimate
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
Solutions for Chapter 10-3: Coefficient of Determination and Standard Error of the EstimateGet Full Solutions
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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
Coeficient of determination
See R 2 .
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
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The variance of the conditional probability distribution of a 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.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
A probability distribution for a discrete random variable
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Error of estimation
The difference between an estimated value and the true value.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
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.