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