REGRESSION MODEL, F AND t- STATISTICS
1. Guideline for regression model
Professor Muhammad Anees commented as such>> 1. Run any regression model. 2. Test the
assumptions 3, Remedy and solve the violation if any through the recommended approaches 4.
re-run the modifyed regression models, and test the assumptions again 5. If any further
violation, again proceed with Step 3 and 4. 6. Do this until you get the corrected form of
regression model free from all violations of all assumptions,
2. When OLS can be used?
Professor Noman Arshed commented about OLS and cointegration as such >> If all variables
are I(0) no cointegration tests are required and OLS can be used.
3. When to use OLS, FMOLS, DOLS, ECM and ARDL model?
Professor Tella Oluwatoba Ibrahim talks about OLS, ECM, VECM Model as such >>>>
Traditionally, Econometric is based on CLassical Ordinary Least Square where we believed
that time-series data have a constant mean and Variance, that is, No series in a regression
model has a unit root. Thus, in a situation,we are faced with purely I(O) series, OLS is the most
appropriate model is OLS. ECM,ARDL, Bounds Test techniques, FMOLS, DOLS etc arises
when the use of OLS breaks down.
4. What is the interpretation of the result?
Professor Akhtar Khan posted the below figure.
Carlos Valdes commented< The F value for the hypothesis "all betas are equal to 0" right below
is the p value...
Sivarajasingham Selliah commented> F test statistics value is for overall significance test.
Kara Brahim commented> the F statitistic of this model equal to 748,88 is greater than F critical
value with ( 3, 19) degree of freedom , meaning that the null hypothesis (all coefficients are
zero ) is rejected , p-value less than 0,05, consequently all coefficients are jointly significant
( the model is good )
Hifsa Syed commnted> F test shows overall significance of the model. Calculated value is
greater than observed value signifying the model is statistically significant.
5. Interpret the results of the regression result below.
Sayed Hossain posted the following figure.
Professor Taiwo Timi commented>The model does not look overall fitted, but can we assume a
situation where both X1 and X3 can not be statistically significant in explaining the dependent
variable. a good example of this is taxation and economic growth in developing African
Professor Akhtar Khan commented> X1 and X3 are insignificant only X2 is significant. R-square
is very low just 16%.Durbin Waston test value are near to 2 means no auto-correlation or serial
correlation. Whole model is not significant because F-test Value is insignificant.
Professor Abubakar Kumo commented> (1) the model does not fit the data well. (2) Only one
variable X2 is significant at 5% level (3) The D.W >2 indicates that there's no autocorrelation or
serial correlation . (4) Given the F-stat and adjusted R2 of just 8 % it means only 8% of the
variation in the dependent variable is explained by the model. This is not good fit. The model
did not fit the data well.
Emine Kılavuz The independent variables which are slected are not correct, they can not
explain changes in the dependent variable.
Gerardo Andrés Milano Gallardo commented> Durbin Watson Stat is nearly two, but there is
just one significant variable. It'd be a multi-collinear case, if I don't get wrong.
Arbab Tahir Khan Here in the three independent variable only one is significant individually the
model is not good fit r square is also low and f state show the relaibality of over all model but his
value is 12.13 here which is more than 5% so the overall model is not good fit
Ernest Tubolayefa commented> Using the DW value, the null of No Positive/Negative
autocorrelation cannot be rejected given the upper bound (du) critical DW value of 1.65 for 35
observation and 3 explanatory variables. Thus, (du _ 4-du) becomes (1.65 _ 2.35). The
calculated DW value of 2.184 falls within (1.65_ 2.35) which is the region we cannot reject the
null. Thus, there is no Positve (or negative) Autocorrelation in the model. For further
explananation, Go to Durbin-Watson table and read off the value for upper limit (du) with 35
observation and 3 explanatory variables (k=3) at 5% sig. Level which is 1.65. For first order
positive serial correlation, the calculated DW must be less than 1.65 but in the above model
calculated DW is 2.184, thus there is no positive serial correlation in the model. On the other
hand, for negative serial correlation, the calculated DW must be greater than (4_du), given that
du=1.65, (4_du) becomes (4-1.65= 2.35) but in the model above, 2.184 < 2.35, thus, there is no
negative serial correlation in the model.
Mosikari Teboho commented> variable X1 and X3 they are not statistically significant, wich
might be a weakness. and our goodness of fit is low, which is a weakness. the strength could
be that the D.W is 2.18 which suggest no serial correlatio
Dada James Temitope commented> only x2 is significant, R2 is very low, which mean the
explanatory variable did not fit the model wel. also, f statistic that measure the overall significant
of the model is not significant.
Sibawaihee Dayyabu commented> Only one variable (i.e. X2) is significance at 5%. The model
is free from the effect of serial correlation because the value of DW is greater than 2 Despite all
these pros, the model is having low prediction power due to lower value of R2 (i.e. 0.087)
6. Features of a regression model
Sayed Hossain posted the figure below.
Tella Oluwatoba Ibrahim commented> But if an explanatory variable doesn't follow economic
theory,I see nothing wrong with it as long as the researcher can justify why variables failed to
follow apiori sign. For instance,the cost push inflation claimed that higher interest rate will raise
the cost of borrowing which in turn leads to higher cost of production. And price is believed to
be a positive function of cost of production(as well as interest rate) in the theory. But if your
model displayed a negative sign,you needn't to use physical alteration but rather provide
justification for such sign. You may say-contrary to the apiori expectation,interest rate exert
negative impact on inflation. This may be attributed to high non- performing loan in the economy
in such a way that a reduction in interest rate encourage the economic agents to borrow but
most component of the loans go into transactional demand which tends to push demand above
what is needed to clear the market
Ayaz Khan commentedd> the last feature mostly cover the other features....
Prabhat Majumdar commented> The model should not have irrelevant variables. Xs must not
be strongly correlated with each other. Causality must be unidirectional and a single relation
should be sufficient. . Exogeneity tests necessary.
Rohin Otieno commented> The regression model should be linear, correctly specified with an
additive error term.
Katji Makatjane commented> all the regression models estimates should be blue.
7. Hello everybody here are my results- my model is time series, all my variables are
significant as you can see, and stationary at first difference, but it suffers from
autocorrelation D.W is lower than du from D.W table. R square is high. as it suffers from
serial correlation as well. I'm beginner in econometrics please need your help, and tell
me how to eliminate autocorrelation?
Barka Ahmed posted the following figure. (Dec 30, 2015)
Saeed Aas Khan Meo commented>Convert your variables into log form and run again
regression and may be increase observations
Gurpreet Singh commented>Here's what I can suggest from my elementary knowledge:
1. Try different functional forms like Log etc. Your model may be misspecified.
2. Try GLS instead of OLS estimation.
Aadil Shah plz sand me base paper and data. i will give u accurate result.Aadilshah777@gmail.
Lim Kim Juan commented> spurious regression-R squared greater than Durbin Watson
Tarek Djeddi commented> Spurious regression. Plz test the Multicolinearity.
Valdemir Galvao de Carvalho commented> the omission of one or more explanatory variables
reflect the waste, whose values tend to be autocorrelated. Poor specification of the
mathematical form: depending on the structure of the data, you must perform an exploratory
analysis of the data so that the most appropriate model to study is chosen. Imperfect adjustment
of statistical series: many published data contains interpolations or smoothing, which may make
random disturbâncias correlated over time. Once diagnosed correlation, it is possible to
eliminate their effects through changes of the variables. To correct the autocorrelation three
methods are: the estimate of Cochrane-Orcutt; two-stage method of Durbin and method of the
Khaled Elbeydi commented> Try log form and if u still have auto correlation add ar(1)
Jabbar Ali Its suprious regreesion bro,, try to increase ur sample size and take log of variables.
Momal Faizan commented> First check correlation among the variables through eviews...n
eliminate those variables having high correlation value... Then do something else
Hassan Danish commented> if your variables are stationery a 1st diff , then why r u applyng
OLS ? move to co-integeration analysis
Tarek Djeddi commented> E_views use LS not OLS which is a method that can't be used in
practice because it can be used only when all stochastic hypothesis are satisfied. And this is
Sayed Hossain commented> Just create 1 period lag of dependent variable(INF) and run the
model again having this lagged INF as independnet variable. I hope your autocorrelation
problem will be solved. We also call it AR(1) process. Even if you write AR(1) as independent
variable and run the model again, autororrelation is likely to be removed.
8. What are the strength and weaknesses of this model?
Sayed Hossain posted the figure below.
Budi Setiawan commented> I'm focusing on durbin watson 1.88 and that value is still in the
range -2<DW<+2 so the conclusion will be no autocorrelation.
Younes Azzouz commented> -2<dw<2 where did you get the formula? Dw is included between
0 and 4
Muhammad Asghar commented> As per DW, no serial autocorrelation because it approaching
to 2, further it may verified that the particular value may not follow in inconclusive zone at this
degree of freedom.
Meher Afroze commented> Large sample size, only two explanatory var, and DW close to 2
implies no serial correlation.
Saeed Aas Khan Meo commented> no serial correlation you also can see serial correlation
through this table,http://saeedmeo.blogspot.com/2015/10/autocorrelation.html
Syed Masroor Hussain Zaidi commented> No autocorelation and serial correlation because dw
is around 2 and the model has no lags
Ansarabbas Abbas commented> you must be put excel file and make a scatter plot of the data.
If the relationship is linear then serial correlation do not exist if scatter plot is nonlinear then
there is serial correlation. Serial correlation is commonly exist in time series data but not in
cross sectional data.
Ansarabbas Abbas commented> numerical figures provide us just clues but not complete
information you must be go to in real world and spending shoe leather
Naila Erum commented> No serial correlation
Hassan Danish commented> numerical values cannot tell us the right picture of AC.. but i think
AC is present in this model, because when errors are serially correlated then value of R2
become very small ..
Ansarabbas Abbas commented> in time series data time plays a significant and as a third
implicit variable between dependent variable and independent variable .the classical
assumption of error tern follows a normal distribution does not fulfill. hence problem of serial
correlation is significant.
Sayed Hossain commented> Only intercept is significant. R square is extremely low, not good
sign. F statistics is not also significant, bad sign too. As DW is close to 2, probably there is no
Meo School of Research
Hossain Academy Note