Topic 4 (Exploring Bivariate Data)

explanatory variable

attempts to explain the observed outcomes

response variable

measures an outcome of a study

scatterplot

displays the relationship between two quantitative variables measured on the same individuals

positive association

high values of the two variables tend to occur together

negative association

high values of one variable tend to occur with low values of the other variable

linear relationship

the points show a straight line pattern, and are an important form of relationship between two variables

strength

is determined by how close the points in the scatterplot lie to a simple form such as a line (strong/weak); description of the relationship of the overall pattern

categorical variables

can be used to plot points on a scatterplot with different colors or symbols

correlation

measures the strength and direction of the linear association between two quantitative variables x and y

residual

the difference between the observed and predicted values of y

influential observations

individual points that substantially change the correlation or the regression line

regression line

A straight line that describes how a response variable y changes as an explanatory variable x changes

Least-squares regression line (LSRS)

the straight line that minimizes the sum of the squares of the vertical distance of the observed y values from the line

predict

the ability to say what is going to happen in the future on the basis of present indication or available date

slope (b)

the rate at which the predicted response changes along the line as the explanatory variable x changes

intercept (a)

the predicted response ŷ when the explanatory x = 0

regression

a process for determining the statistical relationship between a random variable and one or more independent variables that is used to predict the value of the random variable

logarithm

the exponent that indicates the power to which a number is raised to produce a given number

linearly

how a variable grows over time if it adds a fixed increment in each equal time period

exponentially

how a variable grows if it is multiplied by a fixed number greater than 1 in each equal time period. Exponential decay occurs when the factor is less than 1

exponential function

a nonlinear growth that can be modeled by the form y=ab^x

power function

a nonlinear growth that can be modeled by the form y=ax^b

extrapolation

use of a regression line or curve for prediction for values of the explanatory variable outside the domain of the data from which the line or curve was calculated

lurking variable

is a variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied.

experimental

explanatory variable is directly changed and other influences of the response are controlled

form

(linear, curvature, clusters, exponential, etc) the shape the pattern appears to emulate

direction

(positive, negative, etc) where the pattern is going

outliers

data that is an exception to the pattern