Statistical Foundations: Predicting VolatilityFollowing are the major steps we take to estimate volatility, using the S&P 500 Index:
- Let's lo...

Lessons

- CFA L2: Quantitative Methods - Introduction
- Quants: Correlation Analysis
- Quants: Single Variable Linear Regression Analysis
- Standard Error of the Estimate or SEE
- Confidence Intervals (CI) for Dependent Variable Prediction
- Coefficient of Determination (R-Squared)
- Analysis of Variance or ANOVA
- Multiple Regression Analysis
- Multiple Regression and Coefficient of Determination (R-Squared)
- Fcalc – the Global Test for Regression Significance
- Regression Analysis and Assumption Violations
- Qualitative and Dummy Variables in Regression Modeling
- Time Series Analysis: Simple and Log-linear Trend Models
- Auto-Regressive (AR) Time Series Models
- Auto-Regressive Models - Random Walks and Unit Roots
- ARMA Models and ARCH Testing
- How to Select the Most Appropriate Time Series Model?

# Confidence Intervals (CI) for Dependent Variable Prediction

- In all likelihood, your model will not perfectly predict Y.
- The SEE can be extended to determine the confidence interval for a predicted Y value. A common CI to test for a predicted value is 95%.
- Your regression parameters, the y-intercept (b0) and slope coefficient (b1) will need to be tested for significance before you can generate a confidence interval around your model’s project Y value around an expected X value.

- H0 = 0 is the null hypothesis when testing either parameter and you will look to reject this in significance, (note: typically the greater emphasis is on the slope coefficient, as b1 value not statistically different from zero indicates no relationship between Y and X).
- tcalc = the standard script for the output of your significance test on the regression model’s parameters and its absolute value must exceed the designated tcritical on a two tailed significance test.

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