multiplicity

Examples of multiplicity in the following topics:

• Multiple Regression Models

  • Multiple regression is used to find an equation that best predicts the $Y$ variable as a linear function of the multiple $X$ variables.
  • You use multiple regression when you have three or more measurement variables.
  • One use of multiple regression is prediction or estimation of an unknown $Y$ value corresponding to a set of $X$ values.
  • Multiple regression would give you an equation that would relate the tiger beetle density to a function of all the other variables.
  • As you are doing a multiple regression, there is also a null hypothesis for each $X$ variable, meaning that adding that $X$ variable to the multiple regression does not improve the fit of the multiple regression equation any more than expected by chance.

• Foster Pools of Expertise in Multiple Places

• References

  • Multiple Intelligences in the classroom.
  • Teaching and learning through Multiple Intelligences.
  • Problem-based learning and other curriculum models for the Multiple Intelligences classroom.
  • Frames of mind: the theory of Multiple Intelligences.
  • Intelligence reframed: Multiple Intelligences for the 21st century.

• Multiple IRRs

  • When cash flows of a project change sign more than once, there will be multiple IRRs; in these cases NPV is the preferred measure.
  • In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values.
  • There may even be multiple IRRs for a single project, like in the above example 0% as well as 10%.
  • As cash flows of a project change sign more than once, there will be multiple IRRs.
  • Explain the best way to evaluate a project that has multiple internal rates of return

• Future Value, Multiple Flows

  • To find the FV of multiple cash flows, sum the FV of each cash flow.
  • Finding the future value (FV) of multiple cash flows means that there are more than one payment/investment, and a business wants to find the total FV at a certain point in time.
  • The first step in finding the FV of multiple cash flows is to define when the future is.
  • If the multiple cash flows are a part of an annuity, you're in luck; there is a simple way to find the FV.
  • The FV of multiple cash flows is the sum of the future values of each cash flow.

• Addition, Subtraction, and Multiplication

  • Complex numbers are added by adding the real and imaginary parts; multiplication follows the rule $i^2=-1$.
  • The multiplication of two complex numbers is defined by the following formula:
  • The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit.
  • Indeed, if i is treated as a number so that di means d time i, the above multiplication rule is identical to the usual rule for multiplying the sum of two terms.
  • = $ac + bdi^2 + (bc + ad)i$ (by the commutative law of multiplication)

• The Law of Multiple Proportions

  • The law of multiple proportions states that elements combine in small whole number ratios to form compounds.
  • The law of multiple proportions, also known as Dalton's law, was proposed by the English chemist and meteorologist John Dalton in his 1804 work, A New System of Chemical Philosophy.
  • Dalton's law of multiple proportions is part of the basis for modern atomic theory, along with Joseph Proust's law of definite composition (which states that compounds are formed by defined mass ratios of reacting elements) and the law of conservation of mass that was proposed by Antoine Lavoisier.

• Division of Complex Numbers

  • Division of complex numbers is accomplished by multiplying by the multiplicative inverse of the denominator.
  • The multiplicative inverse of $z$ is $\frac{\overline{z}}{\abs{z}^2}.$
  • The key is to think of division by a number $z$ as multiplying by the multiplicative inverse of $z$.
  • For complex numbers, the multiplicative inverse can be deduced using the complex conjugate.
  • So the multiplicative inverse of $z$ must be the complex conjugate of $z$ divided by its modulus squared.

• Introduction: Multiple relations among actors

  • Social relations among actors, however, are usually more complex, in that actors are connected in multiple ways simultaneously.
  • The characteristics and behavior of whole populations, as well, may depend on multiple dimensions of integration/cleavage.
  • To be useful in analysis, however, the information about multiple relations among a set of actors must somehow be represented in summary form.
  • The "reduction" approach seeks to combine information about multiple relations among the same set of actors into a single relation that indexes the quantity of ties.
  • Summarizing the information about multiple kinds of ties among actors as a single qualitative typology is discussed in the section on "role algebra."

• Evaluating Model Utility

  • Multiple regression is beneficial in some respects, since it can show the relationships between more than just two variables; however, it should not always be taken at face value.
  • It is easy to throw a big data set at a multiple regression and get an impressive-looking output.
  • But many people are skeptical of the usefulness of multiple regression, especially for variable selection, and you should view the results with caution.
  • You should probably treat multiple regression as a way of suggesting patterns in your data, rather than rigorous hypothesis testing.
  • For example, let's say you did a multiple regression on vertical leap in children five to twelve years old, with height, weight, age, and score on a reading test as independent variables.