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Error - Essay Example

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Summary
In fact, Standard Error of the mean quantifies how accurately we know the true mean of the population. In our case Standard Errors are very small - a good confirmation of correct C and Beta calculation.
The mean-squared error is one of the most commonly used measures of success for numeric prediction…
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Download file to see previous pages For our companies set we have a good RMSE
Mean absolue error is the average of the difference between predicted and actual value in all test cases; it is the average prediction error. It is similar to RMSE. Again The biggest MAE=0.080486 is for Technitrol, but even this small mean confirms the accuracy of our prediction.
The t-statistic, which is computed as the ratio of an estimated coefficient to its standard error, is used to test the hypothesis that a coefficient is equal to zero. To interpret the t-statistic, you should examine the probability of observing the t-statistic given that the coefficient is equal to zero.
Model parameters significance testing (Student statistics or t-statistics - variate with t-distribution), which is used for coefficient significance estimation in statistical sense, calculates with formula , where model coefficient estimation; null hypothesis (intial hypothesis) relatively to this estimation; Standard Error
In our case, we take null hypothesis that our Beta coefficient is insignificant (). It allows simplifying the calculations, in spite of this hypothesis is opposite to desired (that Beta coefficient is significant) one.
To define whether coefficient estimation is significant, we are to know the sample power (number of observations) (360 in our case), degrees of freedom, where number of model coefficients (n=2 in our case), and of course significance level - let's take as the most popular. In fact, significance level means the error of first kind probability during hypothesis checking.
Let's find the table means for this case.
So, =0.05 and
In Student's distribution table the necessary mean is equal to 1.64 ("more than 60" row).
Let's analyze this result for our companies. The least is 5,01341 for "Parkway Properties". Others are more.
It means, that for all companies Beta-coefficient is significant (t-statistics is more than critical - from the table).
On the other hand, we can provide t-test also for C-coefficient as critical value of t-statistics is the same 1,64.
According to our results, the next companies have C-coefficients, which are not significant (can be not considered in our model).
macdermid
Raytheon
gannett
Navistar
Ecolab
Harsco
Halliburton
That's because the t-statistics for their C - coefficients are less than 1,64.
For other companies these coefficient can't be considered as insignificant as their t-statistics exceeds critical value. They are
parkway properties
Jacobs engineering
jp morgan
Target
Exxon Mobil
technitrol
American Express
National fuel gas
This fact can be explained with some market ...Download file to see next pagesRead More
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