parameter
Algebra
A number or variable in an equation that is considered "known".
Finance
A variable kept constant during an experiment, calculation, or similar.
Psychology
Examples of parameter in the following topics:

Interpreting confidence intervals
 Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability.
 This is one of the most common errors: while it might be useful to think of it as a probability, the confidence level only quantifies how plausible it is that the parameter is in the interval.
 Another especially important consideration of confidence intervals is that they only try to capture the population parameter.
 Confidence intervals only attempt to capture population parameters.

Capturing the population parameter
 A plausible range of values for the population parameter is called a confidence interval.
 If we report a point estimate, we probably will not hit the exact population parameter.
 On the other hand, if we report a range of plausible values – a confidence interval – we have a good shot at capturing the parameter.
 If we want to be very certain we capture the population parameter, should we use a wider interval or a smaller interval?
 Likewise, we use a wider confidence interval if we want to be more certain that we capture the parameter.

ThreeDimensional Coordinate Systems
 A three dimensional space has three geometric parameters: $x$, $y$, and $z$.
 Each parameter is perpendicular to the other two, and cannot lie in the same plane. shows a Cartesian coordinate system that uses the parameters $x$, $y$, and $z$.
 Each parameter is labeled relative to its axis with a quantitative representation of its distance from its plane of reference, which is determined by the other two parameter axes.
 The cylindrical system uses two linear parameters and one radial parameter:
 Identify the number of parameters necessary to express a point in the threedimensional coordinate system

Introduction to confidence intervals
 A point estimate provides a single plausible value for a parameter.
 Instead of supplying just a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter.
 In this section and in Section 4.3, we will emphasize the special case where the point estimate is a sample mean and the parameter is the population mean.
 In Section 4.5, we generalize these methods for a variety of point estimates and population parameters that we will encounter in Chapter 5 and beyond.
 This video introduces confidence intervals for point estimates, which are intervals that describe a plausible range for a population parameter.

Parametric Equations
 ., $x$ and $y$) are expressed in terms of a single third parameter.
 is a parametric equation for the unit circle, where $t$ is the parameter.
 The notion of parametric equation has been generalized to surfaces of higher dimension with a number of parameters equal to the dimension of the manifold (dimension one and one parameter for curves, dimension two and two parameters for surfaces, etc.)
 For example, the simplest equation for a parabola $y=x^2$ can be parametrized by using a free parameter $t$, and setting $x=t$ and $y = t^2$.
 This is a function of the derivatives of $x$ and $y$ with respect to the parameter $t$.

Level of Confidence
 The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
 Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter .
 However, in infrequent cases, none of these values may cover the value of the parameter.
 This value is represented by a percentage, so when we say, "we are 99% confident that the true value of the parameter is in our confidence interval," we express that 99% of the observed confidence intervals will hold the true value of the parameter.
 After a sample is taken, the population parameter is either in the interval made or not  there is no chance.

Estimating the Target Parameter: Point Estimation
 Point estimation involves the use of sample data to calculate a single value which serves as the "best estimate" of an unknown population parameter.
 The point estimate of the mean is a single value estimate for a population parameter.
 A popular method of estimating the parameters of a statistical model is maximumlikelihood estimation (MLE).
 The approach is called "linear" least squares since the assumed function is linear in the parameters to be estimated.
 Contrast why MLE and linear least squares are popular methods for estimating parameters

Review

Estimation
 Estimating population parameters from sample parameters is one of the major applications of inferential statistics.
 One of the major applications of statistics is estimating population parameters from sample statistics.
 It is rare that the actual population parameter would equal the sample statistic.
 Instead, we use confidence intervals to provide a range of likely values for the parameter.
 We know that the estimate $\hat { \theta }$ would rarely equal the actual population parameter $\theta $.

Hypothesis Tests or Confidence Intervals?
 When we conduct a hypothesis test, we assume we know the true parameters of interest.
 When we use confidence intervals, we are estimating the parameters of interest.
 It is worth noting that the confidence interval for a parameter is not the same as the acceptance region of a test for this parameter, as is sometimes assumed.
 The confidence interval is part of the parameter space, whereas the acceptance region is part of the sample space.
 Explain how confidence intervals are used to estimate parameters of interest