Linear Programming A507 Mba
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Determine the best simple regression model for estimating current stock price. Be sure that you indicate your reasoning for selecting the model for me, interpret and evaluate the model.
The best simple regression model for estimating the current stock price is:
Y = 19.93722 + .115048Profits
Reasoning
This was chosen as the best model because, according to the Rsquared values, profit is the most explanatory variable in the data set. Profit also had a p-value less than the given alpha of .10, so profit has a significant relationship with current stock price.
Interpretation
This equation means that for each additional dollar in profits, the current stock price will go up $0.115048. If profit is zero, the current stock price will be $19.93722. So, for example, if profit is $43.20, then:
Y = 19.93722 + .115048(43.20)
Y = 19.93722 + 4.9700736
Y = 24.9072936
So, if profit is $43.20, the current stock price would be $24.9072936.
Evaluation
Overall, the model is not a very good fit. The Rsquared value is only .13785221, so this indicates that only 13.78% of the variability in the stock price can be explained by its linear relationship with profit. The standard error is 18.71360853, so 90% of the actual stock price will be within +/- $18.71360853 of the estimated stock price. The MAPE is 1.1769, which indicates that that, on average, the estimates are off by 117.69%. So, given these values, the model is not a very good fit. In fact, it seems to be a rather poor fit.
Determine the appropriate model (multiple or simple) that best represents the relationship. Be sure that you indicate your reasoning for selecting the model for me, interpret and evaluate the model.
The model that best represents the relationship is a multiple regression model. The equation can be written as:
Y = 15.8199 + -11.354NASDAQ + .103661Profits + .125682Last Years Stock Price + .174888PE Ratio
Note: The model uses NASDAQ relative to all other markets.
Reasoning
The multiple regression model was chosen over the simple regression model because the Rsquared value, Standard error value, and MAPE value indicated that the multiple regression model was a better fit than the simple regression model.
Interpretation
If the stock is traded in NASDAQ and all other variables are held constant, the current stock price will decrease by -$11.354. The model uses NASDAQ relative to all other markets.
If the profits (for the last four quarters) increase by 1 and all other variables are held constant, the current stock price will increase by $0.103661.
If last years stock price (1 year earlier) increases by 1 and all other variables are held constant, the current stock price will increase by $0.125682.
If The Price/Earnings ratio (over the last 4 quarters) increases by 1 and all other variables are held constant, the current stock price will increase by $0.174888.
Evaluation
Overall, the model is not a very good fit. The R squared value is only .315185, so this indicates that only 31.5185% of the variability in the stock price can be explained by the multiple regression model. The standard error is 16.93964875, so 90% of the actual stock price will be within +/- $16.93964875 of the estimated stock price. The MAPE is 1.0943, which indicates that, on average, the estimates are off by 109.43%. So, given these values, the model is not a very good fit.
Identify any potential problems with the data or with the model.
The various data given are given in different and inconsistent time periods. For instance, growth is an annual 3-year growth rate, while sales is given for the last four quarters. This limits how well the data can be fit.
The models Rsquared value is only .315185, which indicates that only 31.5185% of the variability in the stock price can be explained by the model. This is overall not a good percentage, although it was a better percentage than the simple regression models Rsquared value. The MAPE is 109.43%, which indicates that, on average, the estimates are off by 109.43%. Obviously, it is not good for the estimates to be off by an average of 109.43%. The standard error is 16.93964875, so 90% of the actual stock price will be within +/- $16.93964875 of the estimated stock price. The range of the stock price given in the data set only runs from $0.50 to $157.75. The standard error figure indicates that 90% of the actual stock price will be within +/- $16.93964875 of the estimated stock price, so the estimated stock price could be almost $17 off. With a range of only $0.50 to $157.75, a standard error of $17 is not good.
Make suggestions on how to potentially improve the model.
To improve the model, we could first attempt to obtain a better data set that is given over more consistent time periods.
To improve the model, we also could optimize the choice for alpha. We used an alpha of .10 as instructed, but if we had optimized alpha, the overall model may have been better.
Usually, the more information you have to predict something, the better the prediction will be. So, if we had had a larger data set the model could have possibly been better. For instance, we only have the stock price for 2 days Ð- a current price and a price from a year earlier. If we had the stock price for a greater number of days, we possibly would have been able to make a better prediction.
Originally, we had a model that included all original variables from the data set, but some of the variables had high P-values, which indicated that some of the variables were not significant. So, we worked backwards and took the variables with the highest p-values out until we had a model with all significant variables. This helped improve the overall model.
Test for significance of relationships.
The alpha chosen for the model was .10. Our models overall significance (P-value) is 0.00. Because the models P-value is less than alpha, we can conclude that there is a significant relationship somewhere in the model. Each of our independent variables has a P-value less than alpha (.10), so each independent variable is significant. Please see tab “Multiple Regression