Multiple Linear Regression: Multiple Linear Regression: Cloud Seeding Cloud Seeding

By: LailaBy: Laila

RozieRozie

Vimal Vimal

Introduction Introduction

What is Cloud Seeding? What is Cloud Seeding? – Treatment of individual clouds or storm systems to Treatment of individual clouds or storm systems to

achieve an increase in rainfall. achieve an increase in rainfall. – Treatment = massive amount of Silver iodide (100-Treatment = massive amount of Silver iodide (100-

1000g per cloud)1000g per cloud)– The experiment took place in the Florida. The experiment took place in the Florida. – 24 days were considered suitable for seeding on the 24 days were considered suitable for seeding on the

basis of measured suitability criterion S-Ne. basis of measured suitability criterion S-Ne. – optimal days for seeding are those: optimal days for seeding are those:

When seedability is large When seedability is large natural rainfall early in the day is small.natural rainfall early in the day is small.

Objective of the ExperimentObjective of the Experiment

Analyze the data to Analyze the data to see how rainfall is see how rainfall is related to the related to the explanatory variables explanatory variables and determine the and determine the effectiveness of effectiveness of seeding. seeding.

Multiple Linear Regression Multiple Linear Regression

It attempts to model the relationship between two It attempts to model the relationship between two or more explanatory variables, and a response or more explanatory variables, and a response variable by fitting a linear equation to observed variable by fitting a linear equation to observed data. data.

What are explanatory variable? What are explanatory variable? – they are the independent variables in the they are the independent variables in the

experiment used to explain the response variable.experiment used to explain the response variable.

What is the response variable? What is the response variable? – They are the dependent variables. They are the dependent variables.

Explanatory variablesExplanatory variables

Seeding: A factor indicating whether seeding Seeding: A factor indicating whether seeding action occurred: So yes and noaction occurred: So yes and no

Time: number of days after the first day of Time: number of days after the first day of experimentexperiment

Cloud cover: percent cloud cover in that Cloud cover: percent cloud cover in that experimental area. Measure using a radar. experimental area. Measure using a radar.

Prewetness: total rainfall an hour before seedingPrewetness: total rainfall an hour before seeding echo motion: whether radar echo was moving or echo motion: whether radar echo was moving or

stationarystationary SNe: Suitability criteria SNe: Suitability criteria

Response Variable Response Variable

The amount of rain The amount of rain measured in cubic measured in cubic meters * 10meters * 10^7^7

Multiple Correlation CoefficientMultiple Correlation Coefficient

The correlation The correlation between the rainfall between the rainfall and all the explanatory and all the explanatory variables is given by variables is given by the value of Rthe value of R²². .

the set of predictor the set of predictor variables variables XX1, 1, XX2, ... is 2, ... is used to explain used to explain variability of the variability of the criterion variable criterion variable YY

Assumptions Assumptions

All data are drawn from populations following normal All data are drawn from populations following normal distribution distribution

All data are homoskedastic meaning constant variance. All data are homoskedastic meaning constant variance. All explanatory variables are measured without error. All explanatory variables are measured without error. Avoidance of multicolinearily- so when the explanatory Avoidance of multicolinearily- so when the explanatory

variable start to show some correlation among each other. variable start to show some correlation among each other. So it is important to have the correlation between each pair So it is important to have the correlation between each pair of explanatory variables approximates to zero. co linearity of explanatory variables approximates to zero. co linearity is a problem because it can make the regression difficult or is a problem because it can make the regression difficult or misleading to interpret. misleading to interpret.

Multiple Linear Regression ModelMultiple Linear Regression Model

yyi = i = 0 0 + + 11xxi1i1 + + 22xxi2i2 + ... + ... ppxxipip + + εεii for for ii = = 1,2, ... 1,2, ... nn. .

Analysis of varianceAnalysis of variance

The ANOVA calculations for the multiple linear The ANOVA calculations for the multiple linear regression is identical except the degrees of regression is identical except the degrees of freedom are adjusted to reflect the number of freedom are adjusted to reflect the number of explanatory variables in the model. explanatory variables in the model.

There is also an F-test used, which does not There is also an F-test used, which does not indicate which of the parameters indicate which of the parameters x is not equal to x is not equal to zero, but only that atleast one of them is linearly zero, but only that atleast one of them is linearly related to the response variable. related to the response variable.

HomeworkHomework

Define the explanatory variable and Define the explanatory variable and the response variable? (List what they the response variable? (List what they in terms of this experiment) in terms of this experiment)

Explain what each term (variable) Explain what each term (variable) means in the MLR model. means in the MLR model.