Standard Errors of the Beta - Essay Example

The Root Mean Squared Error (RMSE)

The mean-squared error is one of the most commonly used measures of success for numeric prediction. This value is computed by taking the average of the squared differences between each computed value and its corresponding correct value. The root-mean-squared error is simply the square root of the mean-squared error. The root-mean-squared error gives the error value the same dimensionality as the actual and predicted values.  For our company set, we have a good RMSE

For our company, we have a good small(!) RMSE. The biggest RMSE=0.10145 is for Technitrol. All others are less. It means that our prediction is accurate enough

Mean Absolute Error (MAE)

Mean absolute or is the average of the difference between the 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.

t-Statistics

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 the  statistical sense, calculates with formula , where  model coefficient estimation;  null hypothesis (initial hypothesis) relatively to this estimation;  Standard Error

In our case, we take the null hypothesis that our Beta coefficient is insignificant (). It allows simplifying the calculations, despite this hypothesis being 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  several model coefficients (n=2 in our case), and significance level – let’s take  as the most popular. 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 a t-test ala so for C-coefficient as critical 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 McDermid

Rate Gannet

Navistar

Ecolab

Harsco

Halliburton

 That’s because the t-statistics for their C – coefficients are less than 1,64.

parkway properties

Jacob’s engineering

jp morgan

Target

Exxon Mobil

technitrol

National fuel gas

This fact can be explained with some market fluctuations or tax rates which are not considered in CAPM.