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Regression Analysis Of Csd Industry

1835 words - 8 pages

Preview of the Data

The data on the first chart, Nominal Price vs. CSD Sales, will not yield a meaningful linear or logarithmic equation, because the data curves over the Y-axis, which cannot be accurately approximated by either line (or any function of quantity). Therefore, the results from this chart will not be well explained by the line and the R2 value will be low. Further, the upward slope of the data does not conform to the law of demand and thus cannot accurately represent reality. However, the second chart, CSD Sales vs. Real Price, does follow a downward pattern that the linear and logarithmic lines can approximate. Further, because it does not appear to be a hyperbolic concave ...view middle of the document...

|
P-Value | 0.048219708 | Low |
It barely clears the level of significance (<.05), so there’s still a 4.82% chance that the coefficient randomly explains the data (making the true coefficient of P equal to 0). This could be because the coefficient correlates to the data but does not cause the data. |
F-Value | 4.45768351 | Low |
Again, this statistic just barely clears its level of significance (<4), so there a good chance that the equation as a whole describes the data from coincidence alone. This could be because the coefficients don’t accurately represent the data or because the equation is missing other key coefficients. |
Significance of F | 0.048219708 | Low |
This yields the same information as the F-Value: that the equation as a whole is barely significant and that there is a 4.82% chance that the equation’s relationship with the data is pure chance. |
R2-Value | 0.190030849 | Not Significant |
This value is below the .5 threshold for the statistic and suggests that only 19% of the variability in the data is explained by the equation. Therefore, much of the data exists outside the proximity of the line, making the line less representative of the data. |
Intercept Coefficient | 5,904.921297 | N/A |
Nothing can be statistically inferred from this figure. |
Slope Coefficient | 729.7417855 | Not Significant |
Nothing can be statistically inferred from this figure, other than from its slope (discussed above). |
Regression Equation | Q = 5,904.92 + 729.74P | Not Useful |
The equation as a whole is not useful because it did not pass the R2 test and the residuals plot shows a trend. |
|
The residuals show a clear trend following a convex curve. Plus, most of the points could arguably be placed in a cone radiating to the left, as depicted above. Therefore, the regression equation could be improved, so it fails this this test. | The normal probabilities do follow a roughly linear pattern. Thus, it appears that the equation does pass this test. |

Industry Quantity vs. Real Price Regression
Regression Statistic | Value | Significance |
Sign of the Coefficient | Negative | Significant |
This slope conforms to the Law of Demand, stating that quantity demanded will decrease with increasing prices. |
P-Value | 0.00000000002601 | Most Significant |
This value is far below the level of significance (<.05). Thus, it is much easier to conclude that the coefficient is significant. |
F-Value | 188.3478923 | Most Significant |
This is far above its level of significance (>4), making it very unlikely that the equation fits the data by chance. |
Significance of F | 0.00000000002601 | Most Significant |
Similarly, this far below the level of significance (<.05), making it a <.001% chance that the equation randomly describes the data. |
R2-Value | 0.908366563 | Most Significant |
Again, this value is very significant and suggests that the equation explains over 90% of...

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