Multiple Linear Regression:
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.
Objective of the Experiment
Analyze the data to
see how rainfall is
related to the
and determine the
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
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.
Seeding: A factor indicating whether seeding
action occurred: So yes and no
Time: number of days after the first day of
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
SNe: Suitability criteria
The amount of rain
measured in cubic
meters * 10^7
Multiple Correlation Coefficient
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
All data are drawn from populations following normal
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.
Multiple Linear Regression Model
yi = 0 + 1xi1 + 2xi2 + ... pxip + εi for i =
1,2, ... n.
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.
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.