Anova results interpretation

[Rufolo]

Good morning,

I am trying to compare and do an analysis of 13 different funds with an index. All of them belong to latam markets. What i did is obtain different price returns from each month since 2010 and then execute Data Analysis from Excel, so i obtained, from Regression analysis different results and graphs. The problem is i really don't know what do they really mean, not even the graphs.
As i am trying to figure it out and doing some examples last two weeks, i still need help to decipher these results.
So if anybody has time to help me out with this, it is really important to me because i think that understanding to interpretate this data i could do anyone for myself, i'll appreciate so much.

Thanks a lot.

p.s: data is allocated in PCS CHG sheet, and results in Regression sheet.

Kind regards.

 

[ShaktiRathore]

You are here regressing the returns of the 13 so funds against the index returns. Table ` has value of R^2 of 0.997938905 which tells that the following 13 funds explains 99.79% of returns of the equity index. SO that regression explains 99.79% of the index returns with the help of these equity index returns. So this table gives us information of how well the regression is explained by the set of independent variables.
IN the second tables F value is 622.5159622 which is greater than Fcritical at given level of confidence so that this suggests that the given regression is significant or that the 13 equity index returns together explains well the returns on the index. This means atleast one of the coefficient of independent variable is not equal to zero and that these set of independent variables together explains the regression well. We accept the regression model as a whole for predicting the index returns based on the returns of these 13 fund returns.
The third table shows the coefficients of independent variables ie.e fund returns in the multiple regression. Also the fourth column has t values which are used to to test the significance of each of the independent variable in explaining the index returns.
The graphs blue ones i think are the residuals of the regression(difference between the predicted value from regression and the actual value of dependent variable i.e. the index returns) variation w.r.t the variation of the each of the index returns. Try and see if there is some pattern or that some correlation.
The red ones are the variation of the index return w.r.t the variation in each of the fund returns.

thanks

 

[Rufolo]

Wow, first thanks a lot for taking your time analyzing data, very kind of you.
As i expected this is not what i was looking for. I think i should do the regresion for each fund with the benchmark individually. But i wanted to do it as a whole. What i am going to try is do this and then come back with results for two of these funs and make my interpretations, so then you can correct me.

Thanks a lot,

I really appreciate this

 

[Rufolo]

Here i go again.
Attached you'll find an excel with two sheets. One named "Data" which contains monthly returns for the benchmark MN40LAU, and 4 stocks (which represents almost 20% of the benchmark).
So i did Regression with excel and obtained data you'll see in Sheet called "Regression".

I managed to exaplin some of the results and i'd like you people to check if that is correct and to do a deeper analisys with the data i obtained.

So please, have a look at the spreadsheet (the more people the better to make a discussion) and comment or interprete the results please, or the alternatives you'd used instead the stocks, or values i used.

Thanks a lot,

Kind regards.

 

[ShaktiRathore]

hi,
your R^2 interpretation is correct to an extent.
F-statistic the higher the value the higher the chances that the given regression is significant or the the independent variables (here 4 equity returs) are sufficient to explain the returns of the index which is the dependent variable. You can see also from the F significance which is nothing but the p value which is judged as p<significance level(1-CL=1-95%=.05) than our result is significant otherwise if p>significance level(.05) than our result is not significant. At 95% CL p=0.000135441 <.05 that our regression is significant.
Regarding t-stat the higher the value the higher the chances that the given independent variable is significant in explaining the dependent variable the index returns. You can compare given t-stat values to the t-critical values , if t-stat>t-critical(2 tail test) than we reject the null and if t-stat<t-critical(2 tail test) than we accept the null.
TO better judge the significance see the 95% confidence intervals Lower 95%Upper 95% If in between the values of lower and upper bound the interval contains 0 than the given ind variable is not significant and is approx. equal to 0 by our hypothesis testing that is we accept the null hypothesis that the given independent variable is not significant.For e.g. variable1 has confidence interval of -0.2338712410-.626009593 which contains 0 so the variable1 in itself is not significant in explaining the dependent variable. Variable3 as the interval 0.1451948370-.632301671 which doe not contains 0 so that we reject null that coefficient of variable3 is 0 and thus we conclude that variable3 is significant in explaining the dependent variable by itself(as is also evident from the high t-stat value of 3.269568993). The p value column can be interpreted in the same way as above. For e.g. p value of variable3 is 0.002853686<.05 so that reject null and conclude that variable3 is significant in explaining the dependent variable by itself.
From plots it seems that the residuals for each independent variable does not depend on the level of the independent variable and does not show any definite pattern which is ok with our regression. Aso the error terms lies equally above and below in random fashion so that the error terms are not serially correlates. You could see a continuous pattern above or below the axis in case of serial correlation but from the plots i cant identify any such pattern.
IN the normal probability plot the values lies equally above and below the x axis which suggests that the error terms are normally distributed and that Expected value is 0. The variance of error terms also seems constant as evident from plots. These validates some of the assumptions of regression.
thanks

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[Rufolo]

Thanks a lot again Shakti for your very accurate answer! It helps a lot to me so i can understand deeply how this tool works so i can use it in my work.
You've been really helpful,

Thanks a iagn.

Kind regards.