intercept

Examples of intercept in the following topics:

• Slope and Intercept

  • The concepts of slope and intercept are essential to understand in the context of graphing data.
  • If the curve in question is given as $y=f(x)$, the $y$-coordinate of the $y$-intercept is found by calculating $f(0)$.
  • Functions which are undefined at $x=0$ have no $y$-intercept.
  • Analogously, an $x$-intercept is a point where the graph of a function or relation intersects with the $x$-axis.
  • The zeros, or roots, of such a function or relation are the $x$-coordinates of these $x$-intercepts.

• Slope and Y-Intercept of a Linear Equation

  • For the linear equation y = a + bx, b = slope and a = y-intercept.
  • From algebra recall that the slope is a number that describes the steepness of a line and the y-intercept is
  • What is the y-intercept and what is the slope?
  • The y-intercept is 25 (a = 25).

• Slope and Intercept

  • In the regression line equation the constant $m$ is the slope of the line and $b$ is the $y$-intercept.
  • The constant $$$m$ is slope of the line and $b$ is the $y$-intercept -- the value where the line cross the $y$ axis.
  • An equation where y is the dependent variable, x is the independent variable, m is the slope, and b is the intercept.

• Interpreting regression line parameter estimates

  • The slope and intercept estimates for the Elmhurst data are -0.0431 and 24.3.
  • (It would be reasonable to contact the college and ask if the relationship is causal, i.e. if Elmhurst College's aid decisions are partially based on students' family income. ) The estimated intercept b0 = 24.3 (in $1000s) describes the average aid if a student's family had no income.
  • The meaning of the intercept is relevant to this application since the family income for some students at Elmhurst is $0.
  • In other applications, the intercept may have little or no practical value if there are no observations where x is near zero.
  • The intercept describes the average outcome of y if x = 0 and the linear model is valid all the way to x = 0, which in many applications is not the case.

• The Equation of a Line

  • The intercept of the fitted line is such that it passes through the center of mass $(x, y)$ of the data points.
  • Where $m$ (slope) and $b$ (intercept) designate constants.
  • In this particular equation, the constant $m$ determines the slope or gradient of that line, and the constant term $b$ determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
  • Three lines — the red and blue lines have the same slope, while the red and green ones have same y-intercept.

• Statistical Literacy

  • In a discussion about the Dallas Cowboy football team, there was a comment that the quarterback threw far more interceptions in the first two games than is typical (there were two interceptions per game).

• Comparing Nested Models

  • Random intercepts model.
  • A random intercepts model is a model in which intercepts are allowed to vary; therefore, the scores on the dependent variable for each individual observation are predicted by the intercept that varies across groups.
  • This model assumes that intercepts are fixed (the same across different contexts).
  • Random intercepts and slopes model.
  • In this model, both intercepts and slopes are allowed to vary across groups, meaning that they are different in different contexts.

• Inference for linear regression

  • Interpret the slope and intercept in context.
  • Interpret the slope and intercept in context.
  • (c) Interpret the slope and intercept in the context of the application.
  • Intercept: People who are 0 centimeters tall are expected to weigh -105.0113 kilograms.
  • The intercept here is meaningless, and it serves only to adjust the height of the line.

• Introduction to inference for linear regression

  • In this section we discuss uncertainty in the estimates of the slope and y-intercept for a regression line.

• Categorical predictors with two levels

  • The intercept is the estimated price when cond_new takes value 0, i.e. when the game is in used condition.
  • The estimated intercept is the value of the response variable for the first category (i.e. the category corresponding to an indicator value of 0).