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Indietro

WEEK 3

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Termini in questo insieme (20)

  • What is a response variable?

    A response variable is the particular quantity we ask a question about in a study; it is the variable we are interested in studying.

  • What is an explanatory variable?

    An explanatory variable is any factor that can influence the response variable.

  • Define a contingency table.

    A contingency table displays two categorical variables with rows listing categories of one variable and columns listing categories of the other. Each cell shows the count of observations for that category combination.

  • What are conditional proportions in a contingency table?

    Conditional proportions are proportions for categories of the response variable based on the explanatory variable, always summing to 1.0 within each explanatory category.

  • What are marginal proportions in a contingency table?

    Marginal proportions are proportions for each category of a variable based on the total sample size.

  • How can you tell if two categorical variables are associated using a contingency table?

    If the conditional proportions differ considerably between categories of the explanatory variable, there is an association. If proportions are roughly the same, the variables are independent (no association).

  • What is a scatterplot?

    A scatterplot is a graphical display for two quantitative variables, with the explanatory variable on the horizontal axis and the response variable on the vertical axis, showing each observation as a point.

  • What does a positive association look like on a scatterplot?

    A positive association means as the explanatory variable (x) increases, the response variable (y) tends to increase.

  • What does a negative association look like on a scatterplot?

    A negative association means as the explanatory variable (x) increases, the response variable (y) tends to decrease.

  • What is the correlation coefficient r?

    The correlation coefficient r measures the strength and direction of a linear relationship between two quantitative variables, ranging from -1 to +1.

  • What does r = +1, r = -1, and r = 0 indicate?

    r = +1 means perfect positive linear association, r = -1 means perfect negative linear association, and r = 0 means no linear association.

  • Does the correlation coefficient depend on the units of variables?

    No, the value of r does not depend on the units of the variables.

  • What is the regression line equation?

    The regression line equation is \(\hat{y} = a + bx\), where a is the y-intercept and b is the slope.

  • What does the slope b represent in a regression line?

    The slope b represents the amount the predicted response variable changes when the explanatory variable increases by one unit.

  • What does the y-intercept a represent in a regression line?

    The y-intercept a is the predicted value of y when x = 0.

  • What is a residual in regression analysis?

    A residual is the difference between the actual value and the predicted value from the regression line: Residual = actual y - predicted y.

  • What does a positive or negative residual indicate?

    A positive residual means the actual value is larger than predicted; a negative residual means the actual value is smaller than predicted.

  • What is r-squared (r²) in regression?

    r-squared (r²) is the proportion of variation in y explained by the linear relationship with x; values closer to 1 indicate a better fit.

  • What is extrapolation in regression analysis?

    Extrapolation is using a regression line to predict y for x values outside the observed data range, which is risky because the trend may not continue.

  • What are influential observations in regression?

    Influential observations are data points that have a large effect on the regression line, often outliers with extreme x values.