With a lot of interesting quotes and quotations in the field of statistics a thought that has intrigued my mind always is of our very own Saul Barron
"The weather man is never wrong. Suppose he says that there's an 80% chance of rain. If it rains, the 80% chance came up; if it doesn't, the 20% chance came up!"
From that time I have been wondering whether at all statistics helps to predict weather forecasts/rains. Exploring this I stuck up with an interesting article regarding whether at all SPSS helps us to predict rains.
I went through a paper which presents a case study of using SPSS 13.0 in weather prediction. The data were collected from 2001 till 2005 and it was made a prediction of future temperatures encountered in that region. For this, he used two methods provided by SPSS 13.0, such as factor analysis and linear regression.
Introduction
Weather prediction has always being a matter of debate. Every time the MET department advices us to carry umbrellas we end up having no rain and vice-versa. But nevertheless, weather warnings are an important forecast because they are used to protect life and environment.
Starting the MET dept. data, we can use SPSS software for weather forecast. SPSS uses its advanced mathematical and statistical expertise to extract predictive knowledge. Thus, together with data and this software; we can predict the outcomes before they occur.
Case Study
For this application, the public available data provided by Hong Kong Observatory site was used.
The structure of the database was:
date – the year when the data were registered;
month – the month when the data were registered;
Avg_press –average pressure;
Max_Temp – temperature daily maximum;
Avg_Temp – temperatures average;
Min_temp – temperature daily minimum;
Relative_humidity – average relative humidity;
Avg_cloud – average amount of cloud;
rainfall – total rainfall.
The temperatures from the database were registered in Celsius degrees. Then, the database is completed with the data about weather corresponding from 2001 to 2005
Outside of the primary variables, they transformed average temperatures from Celsius degrees in Fahrenheit degrees. The transformation formula is (where C is Celsius and F is Fahrenheit)
F = 9/5*C + 32
Linear Regression
Regression analysis is a statistical tool that can produce data predictions. The basic principle behind regression is to use one or more variables to predict another variable of interest. The predictor variables are known as independent variables and the variable that is being predicted is known as the dependent variable.
In this case, they considered the regression between the atmospheric pressure and the average temperature. There is a predictor variable (Avg_pressure) and a dependent variable avg_temperature
Using SPSS regression linear method, we obtain regression coefficients, as shown below.
Avg_temp = B+ Beta * Avg_pressure
Now in case the atmospheric pressure is registered being 1017.5, we can estimate the average temperature using the relation = 736.274:0.704*1017.5=19.95 .
The values predicted in this way are estimations, while the correlation between variables is not perfect. The error from estimations is not directly proportional with the correlation between variables (the correlation graph points being more far away from the regression right line).
Factor Analysis
Now this is a reductive method in which new factors are built based on existing relationships between variables. A period of time, factor analysis was used only in psychology. After noticing the good results of this method, it was applied in the economic analysis and it has become an established statistical method.
The main challenge of factor analysis is to find variables that have as much variation (information) "common" as possible, so that after concentration little useful information is lost.
Using SPSS, we can apply this method by accessing the menu:
Statistics – Data Reduction – Factor
and the “Factor Analysis window will appear”.
We can select the variables needed, as well as various characteristics of the variables that may be calculated like mean, standard deviation, correlation matrix, and number of factors to be determined, factor score coefficient matrix. The exclusion of the case list wise and the suppression of the absolute values less than 0.10 can be done as well.
After the proper selection of the needed characteristics, we can press the OK button. Beside the results described above, the method output presents the Total Variance Explained, the Component Matrix and the new variables found.
On Extraction Sums of Squared Loadings columns, there are explained variance and Cumulative variance for two factors in the context of initial factorial solution.
Variant explained by each factor is distributed between different factors.
Ex:-
If factor 1 : 56,606% and factor 2 : 25.359%.
Together, they explain 81.964% of the variation of analyzed values.
The rest up to 100% remain unexplained by this model factorial.
On Rotation Sums of Squared Loadings columns, we have the same values, but after the procedure of rotation. A redistribution of variation explained by each of the items:
Ex:-
If factor 1 – 43.324% and factor 2 – 38.640% has been made.
Together, they explain 81.964% of the variation of analyzed values, but with redistributed weights.So, using a rotation method of the redistribution between the two factors has been made
Conclusions
Thus we have seen an interesting case as to how the MET DEPT. gives us the prediction. The present application can forecast an unknown value, on the basis of some real, known values, using techniques that don’t use too many scientific details. Also the factor analysis is important because it reduces a large number of variables into fewer factors. But the question to ask again is, Are this Statistics a substitute to our judgment??
Submitted By
Naresh Adwani
Roll No: - 12033
SIBM Bangalore
Ref:- http://bulletin-mif.unde.ro/docs/20091/13SCHIOPU_DANIELA.pdf
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