AP®︎ Statistics: Unit 5 Flashcards

Data with two quantitative measurements for each individual; each observation is a paired ordered pair (x, y)

A graph of the relationship between two quantitative variables in which each ordered pair is plotted as one point

The explanatory variable is used to explain or predict the response and is placed on the x-axis; the response variable is the variable being explained or predicted and is placed on the y-axis

The four characteristics used for a complete description of a scatterplot

Linear association follows an overall straight-line pattern, while nonlinear association follows a curved or bending pattern rather than a straight line

Positive association means as the explanatory variable increases, the response tends to increase; negative association means as the explanatory variable increases, the response tends to decrease

How closely the points follow the general pattern; described visually as strong, moderate, or weak

A group of points concentrated in one region of the scatterplot and somewhat separated from other groups

A point that lies apart from the main pattern of the scatterplot

Numerical summary of the direction and strength of the linear association between two quantitative variables

Correlation is unit-free, is the same for x with y as for y with x, is not resistant to unusual observations, and is undefined if either variable has standard deviation 0

No linear association means r = 0; perfect linear association means all points lie exactly on a nonhorizontal straight line, with r = 1 for positive slope and r = -1 for negative slope

An association between two variables does not by itself show that changes in one cause changes in the other

ŷ = a + bx; a linear equation that uses one quantitative explanatory variable x to predict the response variable y when the relationship appears approximately linear, where ŷ is the predicted response, a is the y-intercept, and b is the slope

The value of y predicted by the regression line for a given x-value

In a regression equation, b; the change in the predicted response ŷ for a one-unit increase in x

In a regression equation, a; the predicted response when x = 0

Interpolation uses a regression model to predict for an x-value within the observed range of x-values, while extrapolation predicts for an x-value beyond that range and is generally less reliable

Observed minus predicted response: residual = y − ŷ. Positive means the model underpredicts, negative means it overpredicts, and 0 means the point lies on the regression line

Scatterplot of residuals versus x-values or predicted values ŷ, used to check whether a linear model is appropriate

Apparent randomness around 0 supports a linear model; a clear curved or other systematic pattern suggests a linear model is not appropriate

The line ŷ = a + bx for predicting y from x that has the smallest possible sum of squared residuals

Choose the line for which the sum of squared residuals, Σeᵢ², is as small as possible

(x̄, ȳ)

r²; the proportion of variation in the response variable explained by its linear relationship with the explanatory variable

a; the predicted value of the response variable when the explanatory variable x = 0; interpret in context only if x = 0 is meaningful and relevant