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Inferential Statistics: Correlation, Regression & Hypothesis Testing

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Correlation, regression, the normal distribution and hypothesis testing.

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Correlation in statistics

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  1. 1Correlation in statistics
    A measure of the statistical relationship between two variables, indicating how they change together
  2. 2Regression analysis
    A statistical method for modeling and analyzing the relationship between dependent and independent variables to make predictions
  3. 3Linear regression
    A regression method that models the relationship between variables using a linear equation
  4. 4Method of least squares
    A statistical method that minimizes the sum of squared residuals to fit a line or curve to data points
  5. 5Ordinary least squares (OLS)
    The application of the least squares method to linear regression problems
  6. 6Residual in regression analysis
    The difference between an observed value and the value predicted by the regression model
  7. 7Residual sum of squares
    The sum of squared differences between observed values and fitted values; minimized in least squares methods
  8. 8Nonlinear regression
    Regression analysis where the relationship between variables is modeled with a nonlinear function
  9. 9correlation vs causation
    Correlation indicates variables change together, but doesn't prove one causes the other; causation requires controlled experiments
  10. 10Scatter plot used for in statistics
    To visually display the relationship between two variables and identify patterns or correlations
  11. 11Dependent variable in regression
    The outcome variable being predicted or explained (often plotted on the y-axis)
  12. 12Independent variable in regression
    The predictor variable used to explain or predict the dependent variable (often plotted on the x-axis)
  13. 13Polynomial least squares
    A method that describes variance in predictions and handles both linear and nonlinear regression using polynomial functions
  14. 14Error term in a regression model
    The non-deterministic part of the model, also called disturbance or noise, representing unexplained variation
  15. 15Why is least squares differentiable?
    Because it uses squared errors, providing a handy mathematical property for performing regression calculations
  16. 16Least absolute deviations
    An alternative to least squares that gives equal weight to small and large errors instead of emphasizing large ones
  17. 17What contributions did Francis Galton make to statistics?
    He introduced standard deviation, correlation, and regression analysis, applying them to study human characteristics
  18. 18Spearman's rank correlation coefficient
    A non-parametric measure of correlation that assesses monotonic relationships between ranked variables
  19. 19descriptive vs inferential statistics
    Descriptive statistics summarize sample data; inferential statistics draw conclusions about populations from samples
  20. 20Statistical model
    A mathematical representation of relationships between variables used to describe data or make predictions
  21. 21Observational study in correlation research
    A study where data are gathered without manipulation, and correlations between predictors and responses are investigated
  22. 22Experimental study
    A study involving manipulation of variables and measurement to determine if changes affect outcomes
  23. 23Mean squared error (MSE)
    A measure used for obtaining efficient estimators; the average of squared differences between estimates and true values
  24. 24Root mean square error (RMSE)
    The square root of mean squared error, providing error measurement in the same units as the data
  25. 25Fitted curve or line
    The regression line or curve that best represents the relationship between variables according to the chosen method
  26. 26random error vs systematic error
    Random error (noise) varies unpredictably; systematic error (bias) consistently skews results in one direction
  27. 27What role does sample size play in regression analysis?
    Larger samples generally provide more reliable estimates and stronger statistical power to detect relationships
  28. 28Multivariate analysis
    Statistical analysis involving multiple variables simultaneously to understand complex relationships
  29. 29Coefficient of determination (R²)
    A measure of how well the regression model fits the data, representing the proportion of variance explained
  30. 30Heteroscedasticity
    When the variability of residuals is not constant across levels of the independent variable

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