Dr. Shamsuddin Shahid Department of Hydraulics and Hydrology Faculty of Civil Engineering, Universiti Teknologi Malaysia Room No.: M46-332; Phone: 07-5531624; Mobile: 0182051586 Email: [email protected]MAL1303: STATISTICAL HYDROLOGY Non-parametric Regression 11/23/2015 Shamsuddin Shahid, FKA, UTM You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
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Dr. Shamsuddin ShahidDepartment of Hydraulics and Hydrology
Faculty of Civil Engineering, Universiti Teknologi Malaysia
Null Hypothesis, H0 : The intercept is zero, c = 0Alternative Hypothesis, HA: There intercept is not zero, m ≠ 0
If |t(calculated)| > t (critical, α, n-2), Null hypothesis rejected.The change is significant.
If t(calculated) = 0.11t (critical, 0.05, 10) = 2.23
As t(calculated) < t (critical, 0.05, 10), Null hypothesis CANNOT BE rejected. The intercept is NOT significantlydifferent from zero.It can be commented that discharge is notsignificantly different from zero at 95% level ofconfidence when rainfall is zero.
Test of Significance of Intercept
11/23/2015 Shamsuddin Shahid, FKA, UTM
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Leverage is a measure of an "outlier" in the x direction. It is a function of thedistance from the i-th x value to the middle (mean) of the x values used inthe regression.
11/23/2015 Shamsuddin Shahid, FKA, UTM
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One measure of outliers in the y direction is the standardized residual, esi
An extreme outlier is one for which |esi|>3.There should be only an average of 3 of these in 1,000 observations ifthe residuals are normally distributed.
|esi|>2 should occur about 5 times in 100 observations if normallydistributed.
More than this number indicates that the residuals do not have anormal distribution.
Where,
11/23/2015 Shamsuddin Shahid, FKA, UTM
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Observations with high influence are those which have both highleverage and large outliers. These exert a stronger influence on theposition of the regression line than other observations.
There are two most widely used methods to measure the influence ofoutlier in regression equation,
1. Cook's D2. DFFITS
11/23/2015 Shamsuddin Shahid, FKA, UTM
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Situations such as the above frequently arise where the assumptions ofconstant variance and normality of residuals required by Ordinary LeastRegression (OLS) are not satisfied, and transformations to remedy thisare either not possible, or not desirable.
In these situations, alternative methods are better for fitting lines todata.These include:
To determine a confidenceinterval for slope at 95% level ofconfidence (α = 0.05), the tabledcritical value Xu nearest to α/2=0.025 for N = 8 is found to be 16(p=0.031).
1. Smoothing is an exploratory technique, having no simple equationor significance tests associated with it.
2. The most common smooths estimate the center of the data -- theconditional mean or median of Y as X changes.
3. The lack of an equation is a strength in the sense that a smooth isnot constrained by some prior assumption as to the mathematicalfunction of the relationship.
11/23/2015 Shamsuddin Shahid, FKA, UTM
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