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Given the performance of the stock with reference to the NASDAQ stocks it is possible to construct a tree diagram that will help in the analysis of various outes; the tree diagram is as follows:

From the tree diagram we can determine the various probabilities, in this case we determine the probability that a stock that was a remended buy outperformed the NASDAQ stocks, this is derived from simply multiplying the probability of outperforming the NASDQA by the probability that this stock probability of the oute that it was remended, this is simply multiplying 0.75 X 0.42 from the tree diagram above, the result therefore is 0.315, this is the probability that a remended stock outperformed the NASDAQ.

B.in this case we are given the probability that the NASDAQ will rise in any given month is 0.5, we are also provided with information that the performance of any month is independent from other outes, for this reason therefore we assume that the probability function assumes a binomial distribution, this distribution assumes that there exist n identical trials, there are only two possible outes for a trail which include success and failure, the trials are independent where the oute of one trial does not affect the oute of the other trial and finally success is denoted by P and failure is denoted Q.


The model states that the autonomous value of Y is -0.1386 while if we hold all other factors constant and increase the level of x by one unit then Y will increase by 0.852301, if we hold all other factors and increase the level of SMB by one unit then the level of Y will increase by 0.040825, finally if we hold all other factors constant and increase the level of hall by one unit then the level of Y will increase by 0.033091.

The Durbin Watson test value in this case is 0.560967 meaning that there is still autocorrelation, the Durbin Watson test value equal to 2 means that there is no autocorrelation but in our case this value is less meaning that there is autocorrelation. Heteroscedasticity is the violation of the assumption that states that the variance of the error term has a constant variance across observation, it can be detected through the use of graphs where we plot the error terms versus the explanatory variable, also there are other methods such as the park test, cross sectional data is prone to this problem can be resolved by re specify our estimation method.

Multicollinearity is a situation where the explanatory variables are correlated with the explanatory variables, in this situation it can be detected by the presence of high correlation of determination and the presence of t test that show non significance estimated coefficients; it can also be detected by the presence of high pair wise correlation. To correct the presence of Multicollinearity we can drop the problematic variable, re specify the model, acquiring of additional data or the use of a different sample, transformation of data example from general to log form numbers.



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