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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.