Coefficient of Determination
The coefficient of determination R
2
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 NYSE
Index but their impact is small. The remaining change in NYSE Index is explained by the error
term e.

F-Test
An F-test in regression compares the fits of different linear models. Unlike t-tests that can assess
only 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 no
predictors 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. Thus
Model 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 (Y
1
) = -264.827462
+ 5.285135 (CPI) + e
t