Probability and Statistics

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Statistics. Department of Statistics - Texas A&M University. Mathematica Solution for Statistics. Chaîne de khanacademy. Upload Khan Academy Subscription preferences Loading...

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Working... Khan Academy Salman Khan talk at TED 2011 (from ted.com) 3,756,257 views 3 years ago More free lessons at: Khan talk at TED 2011 (from ted.com) Show less Read more New and Noteworthy Play 10:07 The Beauty of Algebra by Khan Academy 1,266,090 views 2 years ago CC 11:15 SOPA and PIPA by Khan Academy 1,504,041 views 2 years ago CC 7:53 Thank You Khan Academy! Other Khan Academy channels. Cross Validation. Next: Blackbox Model SelectionUp: Autonomous Modeling Previous: Judging Model Quality by Cross validation is a model evaluation method that is better than residuals.

Cross Validation

The problem with residual evaluations is that they do not give an indication of how well the learner will do when it is asked to make new predictions for data it has not already seen. One way to overcome this problem is to not use the entire data set when training a learner. Www-stat.stanford.edu/~susan/courses/s200/lectures/lect11.pdf.

Maximum likelihood. In statistics, maximum-likelihood estimation (MLE) is a method of estimating the parameters of a statistical model.

Maximum likelihood

When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters. The method of maximum likelihood corresponds to many well-known estimation methods in statistics. For example, one may be interested in the heights of adult female penguins, but be unable to measure the height of every single penguin in a population due to cost or time constraints.

Assuming that the heights are normally (Gaussian) distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population. MLE would accomplish this by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable (given the model). Principles[edit] Note that the vertical bar in. Poisson distribution. In probability theory and statistics, the Poisson distribution (French pronunciation [pwasɔ̃]; in English usually /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event.[1] The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.

Poisson distribution

For instance, suppose someone typically gets 4 pieces of mail per day on average. The Derivation of the Poisson distribution section shows the relation with a formal definition. History[edit] Definition[edit] A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k =0,1,2,…, the probability mass function of X is given by:[6] where Properties[edit] Mean[edit] Median[edit] Higher moments[edit] If. Mercury.bio.uaf.edu/courses/wlf625/readings/MLEstimation.PDF. People.physics.anu.edu.au/~tas110/Teaching/Lectures/L3/Material/Myung03.pdf. IBM SPSS Statistics 19. Type: Applications > Windows Files: Size: 475.98 MiB (499099798 Bytes) Tag(s):

IBM SPSS Statistics 19

Random assignment. Random assignment or random placement is an experimental technique for assigning subjects to different treatments (or no treatment).

Random assignment

The thinking behind random assignment is that by randomizing treatment assignment, then the group attributes for the different treatments will be roughly equivalent and therefore any effect observed between treatment groups can be linked to the treatment effect and is not a characteristic of the individuals in the group. In experimental design, random assignment of participants in experiments or treatment and control groups help to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Random assignment does not guarantee that the groups are "matched" or equivalent, only that any differences are due to chance. Random assignment facilitates comparison in experiments by creating similar groups.

Example compares "Apple to Apple" and "Orange to Orange". Prediction interval. In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed.

Prediction interval

The distinction between confidence intervals, prediction intervals and tolerance intervals. When you fit a parameter to a model, the accuracy or precision can be expressed as a confidence interval, a prediction interval or a tolerance interval.

The distinction between confidence intervals, prediction intervals and tolerance intervals.

The three are quite distinct. The discussion below explains the three different intervals for the simple case of fitting a mean to a sample of data (assuming sampling from a Gaussian distribution). The same ideas can be applied to intervals for any best-fit parameter determined by regression. Confidence intervals tell you about how well you have determined the mean. EXCEL 2007: Two-Variable Regression Using Data Analysis Add-in. EXCEL 2007: Two-Variable Regression Using Data Analysis Add-in A.

EXCEL 2007: Two-Variable Regression Using Data Analysis Add-in

Colin Cameron, Dept. of Economics, Univ. of Calif. - Davis This January 2009 help sheet gives information on Two-variable linear regression. EXCEL 2007 Basics: Access and Activating Data Analysis Add-in. EXCEL: Access and Activating the Data Analysis Toolpack A.

EXCEL 2007 Basics: Access and Activating Data Analysis Add-in

Colin Cameron, Dept. of Economics, Univ. of Calif. - Davis.