Ch 3.1 & 3.2 Quiz Review

Interpreting slope

Interpreting slope

The predicted [y in context] goes up/down by [slope] for each increase of 1 [x in context]

Interpreting y-intercept

At zero [x in context], the [y in context] is predicted to be [y intercept] [y units]

correlation

a linear association

-describes strength and direction of correlation

-is a number between -1 and 1

-(-1) and (1) only occur if the linear relationship is perfect

-(>0) is a positive linear relationship

-(<0) is a negative linear relationship

-in strong linear relationships, closer to 1 or -1

-in weak linear relationships, closer to 0

correlation coefficient r

Correlation does NOT imply what?

causation

Correlation does NOT measure what?

form

Correlation should only be used to describe what?

Linear relationships

Does correlation have any units?

No

Regression line

-requires there to be an explanatory variable and response variable and it describes how a response variable (y) changes as an explanatory variable (x) changes

-The equation for it is often used to make predictions about the data

-vertical distances that are “leftover” variation in the response variable

-the vertical distance from the actual value to the predicted value

actual y - predicted y

Residuals

positive residual

above the regression line

negative residual

below the regression line

line of best fit that makes the sum of the squared residuals as small as possible

least-squares regression line

Residual plot

-displays the residuals on the vertical axis and the explanatory variable on the horizontal axis

-magnifies the deviations of the points from the lines making it easier to see unusual observations and patterns

-shows a linear model is appropriate if there is no obvious pattern and if the residuals are relatively small