# What is the difference between an outlier and an influential point?

**Outliers And Influential Points**. An

**outlier**is a data

**point**that diverges from an overall pattern

**in a**sample. An

**influential point**is any

**point**that has a large effect on the slope of a regression line fitting the data. They are generally extreme values.

A.

### Do influential points have a large residual?

An outlier is a data

**point**that diverges from an overall pattern in a sample. An outlier**has**a**large residual**(the distance between the predicted value ( ) and the observed value (y)). An**influential point**is any**point**that**has**a**large**effect on the slope of a regression line fitting the data.#### What is the linear interpolation formula?

**Linear interpolation**involves estimating a new value by connecting two adjacent known values with a straight line. If the two known values are (x1, y1) and (x2, y2), then the y value for some point x is:**Linear interpolation**is a straight line fit between two data points.#### What is the Linest function in Excel?

The Microsoft**Excel LINEST**function uses the least squares method to calculate the statistics for a straight line and returns an array describing that line. It**can**be used as a worksheet function (WS) in**Excel**. As a worksheet function, the**LINEST**function**can**be entered as part of a formula in a cell of a worksheet.#### What does Linest stand for?

It turns out that Excel has a particularly convenient utility for carrying out such calculations: A function called LINEST (which stands for**LINE STatistics**).

B.

### What is an influential observation?

In statistics, an

**influential observation**is an**observation**for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regression analysis an**influential**point is one whose deletion has a large effect on the parameter estimates.#### What is the Studentized residual?

In statistics, a**studentized residual**is the quotient resulting from the division of a**residual**by an estimate of its standard deviation. It is a form of a Student's t-statistic, with the estimate of error varying between points.#### What is b0 in regression analysis?

DEFINITIONS: b1 - This is the SLOPE of the**regression**line. Thus this is the amount that the Y variable (dependent) will change for each 1 unit change in the X variable.**b0**- This is the intercept of the**regression**line with the y-axis.#### How does an outlier affect the mean and standard deviation?

Thus, it measures spread around the**mean**. Because of its close links with the**mean**,**standard deviation**can be greatly**affected**if the**mean**gives a poor measure of central tendency.**Standard deviation**is also influenced by**outliers**one value could contribute largely to the results of the**standard deviation**.

C.

### What is a point of high leverage?

**Leverage**(

**statistics**)

**High**-

**leverage points**are those observations, if any, made at extreme or outlying values of the independent variables such that the lack of neighboring observations means that the fitted regression model will pass close to that particular observation.

#### What does the QQ plot tell us?

The**Q-Q plot**, or**quantile-quantile plot**, is a graphical tool to help**us**assess if a set of data plausibly came from some theoretical distribution such as a Normal or exponential. A**Q-Q plot**is a scatterplot created by**plotting**two sets of quantiles against one another.#### What is a probability paper?

The**probability plot**(Chambers et al., 1983) is a graphical technique for assessing whether or not a data set follows a given distribution such as the normal or Weibull. The data are plotted against a theoretical distribution in such a way that the points should form approximately a straight line.#### What are the properties of the normal probability distribution?

In**probability**theory, the**normal**(or Gaussian or Gauss or Laplace–Gauss)**distribution**is a very common continuous**probability distribution**.**Normal distributions**are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose**distributions**are not known.

Updated: 6th December 2019