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# confidence-interval

1. ### P1.T2.20.18. Multiple regression

Learning objectives: Distinguish between the relative assumptions of single and multiple regression. Interpret regression coefficients in a multiple regression. Interpret goodness of fit measures for single and multiple regressions, including R2 and adjusted-R2. Construct, apply and interpret...
2. ### P1.T2.20.17. Hypothesis tests of univariate linear regression model

Learning objectives: Construct, apply, and interpret hypothesis tests and confidence intervals for a single regression coefficient in a regression. Explain the steps needed to perform a hypothesis test in a linear regression. Describe the relationship between a t-statistic, its p-value, and a...
3. ### Confidence interval

I just realized that confidence interval and confidence level are two different things? When we calculate 95% VaR, we get 1.645 whereas if we do 95% confidence interval for Black-Scholes Merton model, we get the z-value for 1.96? Can anyone please illustrate the difference in these two? Many thanks.
4. ### P1.T2.20.14. Hypothesis testing

Learning objectives: Construct an appropriate null hypothesis and alternative hypothesis and distinguish between the two. Differentiate between a one-sided and a two-sided test and identify when to use each test. Explain the difference between Type I and Type II errors and how these relate to...
5. ### YouTube T2-18b Univariate regression: Confidence interval of slope coefficient

The confidence interval (CI) of the slope coefficient is given by β(1) +/- Standard_Error[β(1)]*Z(α), where Z(α) is the student's t or normal deviate based on the desired confidence level; e.g., if the 2-sided confidence level is 95.0%, the Z(0.95) = 1.96. David's XLS: https://trtl.bz/2vEB0aE
6. ### YouTube T2-10 Test of sample mean (Confidence interval, test statistic and p-value)

The explores the answer to Miller's EOC Question #2: "You are given the following sample of annual returns for a portfolio manager. If you believe that the distribution of returns has been stable over time and will continue to be stable over time, how confident should you be that the portfolio...
7. ### P1.T2.718. Confidence in the mean and variance (Miller Ch.7)

Learning objectives: Calculate and interpret the sample mean and sample variance. Construct and interpret a confidence interval. Construct an appropriate null and alternative hypothesis, and calculate an appropriate test statistic. Questions: For the following questions, please feel free to...
8. ### Miller - End of Chapter question - Hypothesis testing and Confidence Intervals

Question 4: Suppose you invest in a product whose returns follow a uniform distribution between −40% and +60%. What is the expected return? What is the 95% VaR? The expected shortfall? Answer: The expected return is +10%. The 95% VaR is 35% (i.e., 5% of the returns are expected to be worse than...
9. ### Confidence Interval for VaR

When calculating a confidence interval for VaR, we need to take into account the bin size (i.e. the width of the rectangles in the histogram bars). Why is it when we increase the bin size, this reduces the length of the confidence interval? I am trying to think about it from an intuitive...
10. ### P1.T2.209 T-statistic and confidence interval

Hi David, 209.2 Over the last two years, a fund produced an average monthly return of +3.0% but with monthly volatility of 10.0%. That is, assume the random sample size (n) is 24, with mean of 3.0% and sigma of 10.0%. Further, the population's returns are normal. Are the returns statistically...
11. ### P1.T2.80.1 Confidence Intervals

Hi BT forum, Need your help, I'm thoroughly confused by this question and its answer - since the calculated t-value equals the critical t at 5%, aren't we saying we are accepting the null hypothesis that the population average refund mu=\$882 (assuming that was the null since alternative is...
12. ### General VAR question and confidence Interval

Hi David, I'm trying to grasp the big picture regarding var. a) In general -- if there were NO exceedes in VAR (supposing you have a VAR model and evaluating the effectiveness of the model), then you would say that the model is not a very good one, and it's set too low, as you would...