Multiple Linear Regression: Cloud Seeding

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Multiple Linear Regression Cloud Seeding

• By Laila
• Rozie
• Vimal

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Introduction

• What is Cloud Seeding?
• Treatment of individual clouds or storm systems
  to achieve an increase in rainfall.
• Treatment massive amount of Silver iodide
  (100-1000g per cloud)
• The experiment took place in the Florida.
• 24 days were considered suitable for seeding on
  the basis of measured suitability criterion S-Ne.
  
• optimal days for seeding are those
• When seedability is large
• natural rainfall early in the day is small.

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Objective of the Experiment

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

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Multiple Linear Regression

• It attempts to model the relationship between two
  or more explanatory variables, and a response
  variable by fitting a linear equation to observed
  data.
• What are explanatory variable?
• they are the independent variables in the
  experiment used to explain the response variable.
• What is the response variable?
• They are the dependent variables.

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Explanatory variables

• Seeding A factor indicating whether seeding
  action occurred So yes and no
• Time number of days after the first day of
  experiment
• Cloud cover percent cloud cover in that
  experimental area. Measure using a radar.
• Prewetness total rainfall an hour before seeding
• echo motion whether radar echo was moving or
  stationary
• SNe Suitability criteria

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Response Variable

• The amount of rain measured in cubic meters
  107

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Multiple Correlation Coefficient

• The correlation between the rainfall and all the
  explanatory variables is given by the value of
  R².
• the set of predictor variables X1, X2, ... is
  used to explain variability of the criterion
  variable Y

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Assumptions

• All data are drawn from populations following
  normal distribution
• All data are homoskedastic meaning constant
  variance.
• All explanatory variables are measured without
  error.
• Avoidance of multicolinearily- so when the
  explanatory variable start to show some
  correlation among each other. So it is important
  to have the correlation between each pair of
  explanatory variables approximates to zero. co
  linearity is a problem because it can make the
  regression difficult or misleading to interpret.

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Multiple Linear Regression Model

• yi ?0 ?1xi1 ?2xi2 ... ?pxip ei for i
  1,2, ... n.

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Analysis of variance

• The ANOVA calculations for the multiple linear
  regression is identical except the degrees of
  freedom are adjusted to reflect the number of
  explanatory variables in the model.
• There is also an F-test used, which does not
  indicate which of the parameters ?x is not equal
  to zero, but only that atleast one of them is
  linearly related to the response variable.

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Homework

• Define the explanatory variable and the response
  variable? (List what they in terms of this
  experiment)
• Explain what each term (variable) means in the
  MLR model.