Describing Relationships [The Practice of Statistics- Chapter 3]

regression line

regression line

A(n) ________ relating y to x has an equation of the form.

Correlation

________ makes no distinction between explanatory and response variables.

Extrapolation

________ is the use of a regression line for prediction outside the interval of values of the explanatory variable x used to obtain the line.

statistical calculation

An observation is influential for a(n) ________ if removing it would change the results.

doesnt guarantee

A value of r close to 1 or −1 ________ a linear relationship between two variables.

slope

B is the ________, the amount by which y is predicted to change when x increases by one unit.

standard deviation

Standardizing a variable converts its mean to 0 and its ________ to 1.

quantitative variables

A scatterplot shows the relationship between two ________ measured on the same individuals.

overall pattern

An outlier is an observation that lies outside the ________.

least squares

The ________ regression line of y on x is the line that makes the sum of the squared residuals as small as possible.

Residual plots

________ help us assess whether a linear model is appropriate.

correlation itself

The ________ has no unit of measure.

Correlation

________ only measures the strength of a linear relationship between two variables, never curved relationships.

regression line

A(n) ________ is a model for the data, much like density curves.

least squares

The mean of the ________ residual is always 0.

Correlation

________ requires that both variables be quantitative.

regression line

A(n) ________ summarizes the relationship between two variables, but only when one of the variables helps explain or predict the other.

Correlation

________ and regression lines describe only linear relationships.

regression line

A(n) ________ is a line that describes how a response variable y changes as an explanatory variable x changes.

Correlation

________ indicates the direction of a linear relationship by its sign: r> 0 for a positive association and r <0 for a negative association.

To describe a scatterplot, follow the basic strategies of data analysis

look for patterns and important departures from those patterns

IMPORTANT

Not all relationships have a clear direction that we can describe as a positive or negative association

Correlation indicates the direction of a linear relationship by its sign

r > 0 for a positive association and r < 0 for a negative association

Like mean and standard deviation, the correlation isnt resistant

r is affected by outliers

residual = observed y

predicted y

= y

y-hat