18 Questions
What is one challenge in establishing causality between a car's age and its sale price?
Controlling for all other factors
In what scenario would we need to compare the sale prices of two identical cars with one being older than the other?
To establish causality between age and sale price
What distribution is assumed for the 'Sale Price' of cars in the dataset discussed?
Normal distribution
What is the mean sale price (μ) assumed in the normal distribution of car sale prices?
$50k
Within how many standard deviations do about 68% of all car sale prices fall from the mean?
1 standard deviation
What is the range within which about 95% of all car sale prices fall from the mean?
Between $30k and $70k
What theorem states that the distribution of sample means will approximate a normal distribution?
Central Limit Theorem (CLT)
How many car sale prices are sampled to calculate the mean sale price in the Central Limit Theorem scenario?
30
Explain how Bayesian Statistics can be used to update beliefs about the mean Credit Score of customers who defaulted.
Bayesian Statistics uses Bayes' rule to update prior beliefs with new evidence, in this case, the credit scores of defaulters, to calculate a new posterior mean and standard deviation.
Describe the purpose of Survival Analysis in predicting customer default probability.
Survival Analysis estimates the probability of a customer not defaulting after a certain number of years.
Explain how Time Series Analysis can help identify patterns in default rates.
Time Series Analysis can help identify patterns like an increase in defaults during economic recessions by analyzing the number of defaults recorded each year.
How does Principal Component Analysis (PCA) relate Age, Annual Income, and Credit Score in identifying variance?
PCA identifies the first principal component (PC1) as a weighted combination of Age, Annual Income, and Credit Score that captures the most variance in the dataset.
Explain how the Central Limit Theorem (CLT) impacts the distribution of average Credit Scores from samples.
CLT ensures that the average Credit Score across samples will follow a normal distribution, regardless of the original distribution shape.
In Design of Experiments, how can randomly assigning a new scoring system to customers help analyze default rates?
Randomly assigning a new scoring system to customers allows for comparing default rates between the new scoring system group and the control group.
How does the Logistic Regression formula predict the probability of customer default?
The formula predicts the probability of default by considering Age, Annual Income, and Credit Score coefficients in a logistic function.
Explain how the Survival Function differs from traditional probability distributions in predicting default probability.
The Survival Function estimates the probability of not defaulting after a certain time, focusing on time-to-event rather than instantaneous probability.
How does Bayesian Statistics combine the prior belief with observed data to update estimates of the mean Credit Score for defaulters?
Bayesian Statistics uses Bayes' rule to combine the prior belief (prior distribution) with the likelihood function (observed data) to calculate the posterior distribution, updating the mean Credit Score estimate.
Explain the importance of Principal Component Analysis (PCA) in reducing dimensionality for Age, Annual Income, and Credit Score variables.
PCA helps in reducing the dimensionality by finding a weighted combination of the original variables that captures the most variance, simplifying the analysis process.
Learn how to interpret regression analysis coefficients in Excel output. Understand the significance of coefficients, standard errors, t-Stats, P-values, and confidence intervals for independent variables. Explore key summary statistics like R Square and Adjusted R Square.
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