# Negative relationship

inverse relationshipinversely relatednegative correlationanti-correlationanticorrelationnegatively associatedanticorrelatedcorrelates negativelyinverse correlationnegative
In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with lower values of the other.wikipedia
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### Pearson correlation coefficient

correlation coefficientcorrelationPearson correlation
Negative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the arc of separation of the points on the sphere.
The correlation coefficient is negative (anti-correlation) if X i and Y i tend to lie on opposite sides of their respective means.

### Statistics

statisticalstatistical analysisstatistician
In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with lower values of the other.

### Correlation and dependence

correlationcorrelatedcorrelate
A negative relationship between two variables usually implies that the correlation between them is negative, or — what is in some contexts equivalent — that the slope in a corresponding graph is negative.

### Slope

A negative relationship between two variables usually implies that the correlation between them is negative, or — what is in some contexts equivalent — that the slope in a corresponding graph is negative.

### Multivariate random variable

random vectorvectormultivariate
Negative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the arc of separation of the points on the sphere.

### Trigonometric functions

cosinetrigonometric functiontangent
Negative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the arc of separation of the points on the sphere.

### Antipodal point

antipodeantipodalantipodal points
Diametrically opposed points represent a correlation of –1 = cos(π).

### Cross-sectional data

cross-sectionalcross-sectioncross section
An example would be a negative cross-sectional relationship between illness and vaccination, if it is observed that where the incidence of one is higher than average, the incidence of the other tends to be lower than average.

### Time series

time series analysistime-seriestime-series analysis
Similarly, there would be a negative temporal relationship between illness and vaccination if it is observed in one location that times with a higher-than-average incidence of one tend to coincide with a lower-than-average incidence of the other.

### Proportionality (mathematics)

proportionalinversely proportionalproportion
A particular inverse relationship is called inverse proportionality, and is given by y = k/x where k > 0 is a constant.

### Constant (mathematics)

constantconstantsConstant functions
A particular inverse relationship is called inverse proportionality, and is given by y = k/x where k > 0 is a constant.

### Cartesian coordinate system

Cartesian coordinatesCartesianaxes
In a Cartesian plane this relationship is displayed as a hyperbola with y decreasing as x increases.

### Hyperbola

hyperbolicrectangular hyperbolahyperbolas
In a Cartesian plane this relationship is displayed as a hyperbola with y decreasing as x increases.

### Finance

financialfinancesfiscal
In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.

### Rate of return

returnreturnsreturn on investment
In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.

### Financial risk

riskinvestment riskfinancial
In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.

### Diversification (finance)

diversificationdiversifieddiversify
In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.

### Diminishing returns

law of diminishing returnsincreasing returnsdiminishing marginal returns
* Diminishing returns

### Oklahoma State University–Stillwater

Oklahoma StateOklahoma State UniversityOklahoma A&M College
* Michael Palmer Testing for correlation from Oklahoma State University–Stillwater

### Relapse

recurrencerelapsingrecurrent
The D2 receptor availability has an inverse relationship to vulnerability to the reinforcing effects of the drug.

### Mathematical anxiety

math phobiamathematical anxiety and phobiamathematics anxiety
In fact, Ashcraft found that the correlation between math anxiety and variables such as confidence and motivation are strongly negative.

### Axiom of Cumulative Inertia

There is thus a clear negative correlation between the amount of time a person has lived in a certain location, and the likelihood they will move in future.

### Impact event

impactasteroid impactmeteorite impact
There is an inverse relationship between the size of the object and the frequency of such events.

### Law of demand

demand theoryif the price was right
In microeconomics, the law of demand states that, "conditional on all else being equal, as the price of a good increases, quantity demanded decreases ; conversely, as the price of a good decreases, quantity demanded increases ". In other words, the law of demand describes an inverse relationship between price and quantity demanded of a good.

### Baldwin effect (astronomy)

The Baldwin effect in astronomy describes a relationship between continuum and emission-line fluxes observed in the electromagnetic spectra of quasars and active galactic nuclei, namely an anticorrelation between the equivalent width, W λ, of a spectral line and the continuum luminosity, L, in broad UV optical emission lines.