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Statistics for Business - Exam 2 Study Guide

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Terms in this set (21)

  • What is a scatterplot?
    A scatterplot displays pairs of values for two numerical variables, showing the relationship between an explanatory variable (x) and a response variable (y).
  • What are the four features to describe in a scatterplot?
    Direction (positive/negative), form (linear/curved), variation (tightness of points), and outliers (unusual points).
  • What does covariance measure?
    Covariance measures the direction and amount of linear association between two variables but depends on their units.
  • What is correlation (r)?
    Correlation is a standardized measure of linear association between −1 and +1, indicating direction and strength without units.
  • Interpret correlation values: r = 1, r close to 0, r = −1.
    r = 1: perfect positive linear association; r close to 0: little linear association; r = −1: perfect negative linear association.
  • What does r = 0 mean?
    r = 0 means no linear association, but variables could still have a curved relationship.
  • What is the standardized form of the correlation line?
    The line is \(\hat{z}_y = r z_x\), where slope equals r and z-values are standardized.
  • What is the slope-intercept form of the regression line?
    The line is \(\hat{y} = a + b x\), where a is the intercept and b is the slope.
  • How to interpret the slope in regression?
    The slope b predicts the average change in y for a one-unit increase in x.
  • What is spurious correlation?
    An association caused by a lurking variable, not a direct causal relationship between the two variables.
  • What is the least squares regression line?
    The line that minimizes the sum of squared residuals, summarizing how the average response y changes with x.
  • How to calculate a residual?
    Residual = actual value − predicted value (\(e = y - \hat{y}\)).
  • What does a residual plot show?
    It shows residuals versus x; a good linear model has residuals scattered around zero with no pattern.
  • What does R-squared (R²) represent?
    R² is the fraction of variation in y explained by the regression line.
  • What is residual standard deviation (sₑ)?
    sₑ measures the typical size of prediction errors left unexplained by the model, in y's units.
  • What does a small p-value indicate in regression?
    Strong evidence against the null hypothesis that the population slope is zero, suggesting a linear relationship.
  • What are the conditions for simple linear regression?
    No lurking variable, linear pattern in scatterplot, random residual variation with no pattern.
  • What is heteroscedasticity?
    Residual variation changes across x-values, often seen as a fan-shaped residual plot.
  • What is high leverage in regression diagnostics?
    An observation with an unusual x-value that can disproportionately influence the regression line.
  • What does the Durbin–Watson test detect?
    It tests for autocorrelation in residuals; a value near 2 indicates no autocorrelation.
  • What is the difference between a confidence interval and a prediction interval?
    Confidence intervals estimate population coefficients; prediction intervals estimate where a new response may fall.