Geomatics Engineering for Transportation (GET)

Assignment # 01:

Submitted To:

Engr. Bilal Zia Malik

Submitted By:

Abdul Azeem

(2011-TE-43)

Department of Transportation Engineering and Management UET,Lahore

ContentsWhat is Regression? ............................................................................................................................................ 2

What are Types of Regression? ....................................................................................................................... 2What is the difference between dependent and independent variables? ..................................................... 2

What is Root Mean Square (RMS) error?............................................................................................................ 2What is Buffer Zone?........................................................................................................................................... 3What are different types of Data?....................................................................................................................... 3References:.......................................................................................................................................................... 4

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What is Regression?

A statistical measure that attempts to determine the strength of the relationship between onedependent variable (usually denoted by Y) and a series of other changing variables (known asindependent variables).What are Types of Regression?There are two basic types of regression

1. Linear RegressionLinear regression uses one independent variable to explain and/or predict the outcome of dependentVariable.General form:

Y = a + bX + u2. Multiple Regression

Multiple regression uses two or more independent variables to predict the outcome of dependentvariable.General form:

Y = a + b1X1 + b2X2 + B3X3 + ... + BtXt + u

Where:Y= the variable that we are trying to predictX= the variable that we are using to predict Ya= the interceptb= the slopeu= the regression residual.

In regression, the R2 coefficient of determination is a statistical measure of how well the regressionline approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits thedata.

What is the difference between dependent and independent variables?In any phenomenon or experiment, the dependent variable is the one which value depends upon someother variable known as independent variables which on the other hand do not depend upon thedependent variables. In any case of observations there can be more than one independent variableswhile there is chosen only one dependent variable for observational purposes.

The dependent variable is plotted on Y axis, while the independent variable is plotted against X axis.

What is Root Mean Square (RMS) error?A kind of average sometimes used in statistics and engineering, often abbreviated as RMS. To findthe root mean square of a set of numbers, square all the numbers in the set and then find the arithmeticmean of the squares. Take the square root of the result. This is the root mean square.

IN GIS TERMS:

Acronym for root mean square error. A measure of the difference between locations that are knownand locations that have been interpolated or digitized. RMS error is derived by squaring the differences

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between known and unknown points, adding those together, dividing that by the number of test points,and then taking the square root of that result.

Significance and Example:

Root Mean Square Error (RMSE) (also known as Root Mean Square Deviation) is one of the mostwidely used statistics in GIS. RMSE can be used for a variety of geostatistical applications.

RMSE measures how much error there is between two datasets. RMSE usually compares a predictedvalue and an observed value. For example, a LiDAR elevation point (predicted value) might becompared with a surveyed ground measurement (observed value). Predicted value: LiDAR elevation value Observed value: Surveyed elevation value

Root mean square error takes the difference for each LiDAR value and surveyed value. You can swapthe order of subtraction because the next step is to take the square of the difference. (The square of anegative or positive value will always be a positive value). Divide the sum of all values by the numberof observations. This is how RMSE is calculated.

What is Buffer Zone?A buffer is an area defined by the bounding region determined by a set of points at a specifiedmaximum distance from all nodes along segments of an object.A buffer in GIS is a zone around a map feature measured in units of distance or time. A buffer isuseful for proximity analysis.

These zones or buffers can be used in queries to determine which entities occur either within or outsidethe defined buffer zone.

Buffer zones can also be used to check the proximity of different spatial points on the map.

What are different types of Data?There are two basic data types of data:

1. Qualitative data2. Quantitative data

There are also some types of data such as

Categorical data Ordinal data

1. Qualitative Data:It is the data that is not given numerically. It shows the qualities of the objectse.g. the color of the geographical data collected of a region

2. Quantitative Data:These data have meaning as a measurement, such as a persons height, weight, IQ, or blood pressure;or theyre a count, such as the number of stock shares a person owns, how many teeth a dog has, orhow many pages you can read of your favorite book before you fall asleep.

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Quantitative data has further two types:2.1. Discrete Data:

It represent items that can be counted; they take on possible values that can be listed out. The list ofpossible values may be fixed (also called finite); or it may go from 0, 1, 2, on to infinity (makingit countably infinite).Discrete data in GIS can be the number of local roads in a given patch of land under observation

2.2. Continuous Data:

Continuous data represent measurements; their possible values cannot be counted and can only bedescribed using intervals on the real number line. For example, the exact amount of gas purchased atthe pump for cars with 20-gallon tanks would be continuous data from 0 gallons to 20 gallons,represented by the interval [0, 20], inclusive. You might pump 8.40 gallons, or 8.41, or 8.414863gallons, or any possible number from 0 to 20.

Continuous data can be represented by the total length of the roads in a given project.

References:http://www.investopedia.com/terms/r/regression.asphttp://libraries.mit.edu/files/gis/regression_presentation_iap2013.pdfhttp://www.mathwords.com/r/root_mean_square.htmhttp://support.esri.com/en/knowledgebase/GISDictionary/term/RMS%20errorhttp://gisgeography.com/root-mean-square-error-rmse-gis/www-users.cs.umn.edu/~npramod/pramod_enc_bib.doc

http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i11/bk7_11i1.htm

http://www.dummies.com/how-to/content/types-of-statistical-data-numerical-categorical-an.html