Stock Return Analysis and Statistical Concepts

Posted by on Dec 15, 2024 in Mathematics | 0 comments

Stock Comparison: Return and Risk

Stock 1: x̄ = 9.62% and s = 23.58%

Stock 2: x̄ = 12.38% and s = 15.45%

x̄ represents the average return of a stock.

Stock 2 has a higher average return because its x̄ (12.38%) is greater than Stock 1’s x̄ (9.62%).

Stock 1 is riskier. Standard deviation (s) measures return volatility. A higher standard deviation indicates wider fluctuations and greater unpredictability. Therefore, Stock 1 is riskier (s = 23.58%) than Stock 2 (s = 15.45%).

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Implication: Sharpe Ratio

Stock

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Statistical Sampling and Analysis Techniques

Posted by on Dec 8, 2024 in Mathematics | 0 comments

Correlation Coefficients

Pearson Correlation Coefficient (r)

Measures the strength and direction of the linear relationship between two continuous variables.

Key Characteristics

  • Range: r values range from -1 to +1.
  • r = +1: Perfect positive linear relationship.
  • r = -1: Perfect negative linear relationship.
  • r = 0: No linear relationship.

Formula: FDg8rAAAAAElFTkSuQmCC

Assumptions: Variables are continuous and normally distributed. The relationship between variables is linear. No significant outliers.

Applications: Assessing the

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Statistical Analysis of Data Distribution and Correlation

Posted by on Nov 13, 2024 in Mathematics | 0 comments

IntervalClass Mark (Xi)Mean (X)Momentum in n and n = number raised to the pointPearson
Linf – Lsup

(Linf + Lsup) / 2

(xi – X)

(xi – X) * nfi

b2 =

moment4 /

(σ2)2 (where σ2 is the population variance)

Formula

Data Distribution Analysis

The Pearson coefficient (B2) is based on the fourth moment about the mean.

For example, for samples of size 40:

  • If B2 < 2.15, the distribution is negatively skewed (platykurtic).
  • If B2 > 3.99, the distribution is positively skewed.
  • If B2 > 3, the distribution is more pointed
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Understanding Regression Analysis and Variable Relationships

Posted by on Nov 12, 2024 in Mathematics | 0 comments

Relationship Between Variables and Regression: The term “regression” was introduced by Galton in his 1889 book Natural Inheritance, referring to the universal law of regression: each peculiarity in a person is shared by their descendants, but on average, to a lesser degree (regression to the mean). His work focused on describing the physical traits of descendants (a variable) based on their parents (another variable).

Pearson (Galton’s friend) conducted a study of over 1,000 households, examining

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Test Validity and Reliability

Posted by on Oct 16, 2024 in Psychology and Sociology | 0 comments

True or False

V The validity coefficient cannot be higher than the index of reliability.

V The validity coefficient is affected by the reliability of the criterion.

F The standard error of estimate is the difference between obtained and predicted scores.

F The coefficient of validity is an indicator of the stability of scores.

F The validity coefficient of a test is independent of the homogeneity of the sample.

F The validity coefficient expresses the correlation between two parallel forms of a test.

V

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