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Multiple Linear Regression: Cloud Seeding By: Laila Rozie Rozie Vimal 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 * 10^7

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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 + 1 x i1 + 2 x i2 +... p x ip + ε i 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.

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