Coefficient of DeterminationThe coefficient of determination R2 tells the percentage of variation in NYSE Index which is explained by Inflation. In this case the value of 0.9121 suggests that 91.21% of variation in NYSE Index is explained by the CPI. However there might be various other factors that affect the NYSEIndex but their impact is small. The remaining change in NYSE Index is explained by the error term e.
F-TestAn F-test in regression compares the fits of different linear models. Unlike t-tests that can assessonly one regression coefficient at a time, the F-test can assess multiple coefficients simultaneously.The F-test of the overall significance is a specific form of the F-test. It compares a model with nopredictors to the model that you specify. A regression model that contains no predictors is also known as an intercept-only model. In this case, the f test value is 384.172584 which is much greater than the table F value is which is somewhere around 4 for 95% confidence interval. ThusModel is significant.Thus, we can interpret following things from the model:1. Results show that the two variables- NYSE Index and Inflation have a statistically-significant relationship between the two variables. It shows correlation—not causality.2. By regressing NYSE Index on the CPI, we see that the two have a positive linear relationship—an increase in the inflation rate, as measured by the CPI, corresponds to an increase in the level of NYSE Index.3. Per our model, a one-point increase in CPI corresponds to a 61.26 predicted increase in the NYSE Index level.4. Linear regression provides a statistically-significant model estimating variation in the level of NYSE across levels of consumer prices.Discussion & Conclusion Regressing gold prices on the Consumer Price Index across the years 1977-2015 produces the following linear model:Gold Price (Y1) = -264.827462+ 5.285135 (CPI) + et
The analysis of hedging New York Stock Exchange against Inflation gives the following regression:NYSE (Y1) = -4981.348053 + 61.257243 (CPI) + etFrom the analysis, we can clearly say that both the New York Stock Exchange as well as GoldPrices are highly dependent upon the Consumer Price Index(CPI). Still the CPI explains differentproportions of variations in the Gold Prices and NYSE Index.In case of NYSE, the Consumer price Index is highly affecting the NYSE Index with more than91% of change coming out of the sole factor –Inflation. The major reason for this is that theNYSE Index is just comprised of 30 Stock prices only. Their quantities are not taken into account.A change in those prices of 30 stocks which reflect the economy as a whole in a great sense issimilar to change in the overall price level or the inflation. Due to this, the correlation betweenCPI and NYSE is high. However it is not the only factor. Any other factors affect the stock index.