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(1)
number of observations: It must be
greater than the 'number of
Number of variables plus 1'. Here we want to estimate
for 1 variable only, so number of observations must be 3 or more , and we have
41 observations it is good.
It is better to
have Large number of observations to get a good result. (like 100 or more
observations. (The larger the better )
(2) and (3)
C is the constant and its value is 0.155798. This result
says that if there is no X, or say if X is zero then, value of Y is 0.155798.
(4)
0.422690 is standard error of 0.155798. Standard error
measures how reliable the coefficient 0.155798 is. you can perform hypothesis
test for 0.155798 and confidence interval with this value later. (The smaller the better)
(5)
0.368588 is
t-Stattistic for coefficient 0.155798
If you divide coefficient
by its standard error you will get its t-statistic. 0.155798/0.422690=0.368588.
So 0.368588 is the t-Stattistics for 0.155798
T statistics tells us whether coefficient is significant or
not. If absolute t-statistics (without
positive or negative sign) is greater than the critical value of T distribution
then coefficient is significant. Insignificant otherwise. For instance, t-critical
value for 41 observations and two parameters is 1.685 . since 0.368588 is not
greater than 1.685 the coefficient 0.155798 is not significant. However, for now you don’t need to perform tests using t-statistics because Eviews calculates P-values for you
which is easier to calculate the significance .
(6)
0.7144 is P-value of t-Statistics
It tells us whether the coefficient is significant or not.
It is easier than the (5) If P-value is 0.01 or smaller than 0.01 then,
coefficient is significant at 1% level meaning that the estimated coefficient
is very strongly significant. And if it is 0.05 or smaller than 0.05 than the
coefficient is also strongly significant at 5% level. If it is 0.10 or smaller, then, the coefficient is
significant but not so strong as previous two. In the table P-value is 0.7144
which means that the of 0.155798 is not significant.
(7)
X is independent variable,
the variable whose effect on Y you want to test
(8)
The coefficient for the independent variable. It is the most
important part of this table. It tells us how much the dependent variable
change if the X change 1 unit. The estimated value 1.025555 means that if X
increase by 1 unit the Y increases by 1.025555 unit and if X decreases by 1
unit the Y decreases by 1.025555 unit. Please note, the coefficient is
positive it means the relation between X
and Y is positive or X has a positive effect on Y . If you find a negative
value then it means they have a negative relation or X has negative impact on
Y.
(9) standard error for 1.025555. same explanation as (4)
(10) T-statistics
for 1.025555. same explanation as (5)
(11) P-value of T-statistics (1.025555) same
explanation as (6)
note, here P-value is
0.0000 this is smaller than 0.01. it implies that the the coefficient 1.025555 is strongly significant
(at 1% significant level). Now you can say variable X significantly affects Y, or Variable X has a
statistically significant effect on Y.
(12) R-squared :
It is always between
0 and 1 and generally positive. It tells you how much successful your model
is in predicting . A higher R-square is better. In very poor model R
square is close to zero like 0.03 etc. R-squared is found to be 0.79193. it implies that about 79% of changes in Y are explained by the
changes in independent variable X.
(13) Adjusted r square :
It is always equal to or smaller than the R-squared. It does the same job as
R-squared does, measuring how much good your model is in predicting. But it has a Specialty , that is, if you add
more variable even irrelevant variable R squre incresase but adjusted r squae doesn’t. Therefore adjusted R square is kind
of smarter than the R square ;)
The higher the adjusted r square (close
to 1) the better the model. Sometimes
in a very poor model adjusted R-square
become negative . A negative r square is considered as zero r square .
(14) and (14) S.E. of regression and Sum squared resid. :
Both measure how much the estimated Y differ from actual Y (
actual Ys are the value of Y in Y series
of your data file). Of course, you know, it is not good if they differ too far
from each other. A smaller S.E. of regression and a smaller Sum squared resid are the
better for any model.
Note: S.E. of regression
is calculated by dividing the Sum squared resid with df hence, In a regression with very
large number of observation S.E. of
regression become very small.
(15) Log
likelihood:
It is useful when you
compare two nested models. You’ll always find this value negative. a higher value is better for example -40 is
better than -90. A negative value but closer to zero indicates a best fitting model. And you
will choose a model from two models that
has a higher log-likelihood.
(16) F-statistic :
It is used for
testing the overall significance of a model specially in a model where
independent variables are more than one. Do all the independent variables in the model
significantly affect the dependent
variable ? F-statistics will answer this question. If F-statistics is greater than the F-critical then you can
say that all the variables are significant . (the F-critical values are available in last pages of
Econometrics and Statistics books)
(17) Prob(F-statistic):
However you don’t need to check F-statistic and F-critical
value. By looking to the
Prob(F-statistic) you can easily check overall significance of all independent
variables. If the Prob(F-statistic) is equal or smaller than 0.01 you can say
that all the variables jointly in the model significantly affect dependent
variable at 1% significance level. If it
is equal or smaller than 0.05 you can say that all the variables jointly in the
model significantly affect the dependent variable at 5% significance level. And
if it is equal to or smaller than 0.10 this time you can say that all the variables jointly in the
model are significantly affect dependent variable at 10% significance level.
(18) Mean dependent var:
simply it is the average of Y the dependent variable.
(19) S.D. dependent var :
it measures how much the
values of Y differe from its average value.
(20)Akaike info
criterion (21)Schwarz criterion (22)Hannan-Quinn criter :
They are calculated with almost same formulas using
log-likelihood and are called MODEL SELECTION CRITERIA. Smaller values
are preferred. If you have different models to compare, A preferred model is
the model with smaller value of (AIC), (SC)
and (HQ) or with smaller value of any two of them. However AIC is best used for Time series models.
(24) Durbin-Watson stat:
It tells us whether
our model suffer ‘serial correlation problem’
If it is close to
2 ; No serial correlation in the model
If it is close to 0 ; positive correlation in the model
If it is close to 4 ; Negative correlation in the model
It is better if we get the Durbin-Watson stat near
to 2 such as 1.70, 2.01, 2.20 etc. In our model we found 1.69882 indicating no
serial correlation in the model.
Important Note !
The purpose of this post is to give the basic idea about the results of a simple regression model computed by Econometric software. (I have used Eviews). So, some of my comments about some results are too straightforward. For example a ''higher R-square is better'' does not make sense if you are dealing with non-stationary variables.
The purpose of this post is to give the basic idea about the results of a simple regression model computed by Econometric software. (I have used Eviews). So, some of my comments about some results are too straightforward. For example a ''higher R-square is better'' does not make sense if you are dealing with non-stationary variables.