fitness

Examples of fitness in the following topics:

• Tactics for Improving Fit

  • The first step in improving fit for a given job design is training.
  • Job analysis employs a series of steps which enable a supervisor to assess a given employee/job fit and to improve the fit, if necessary.
  • Observation: The simplest method of assessing how a job and employee fit is observing the employee at work.
  • Checklist: Another method of improving job fit is to create a checklist.
  • Employee questionnaires can be a useful method of assessing job fit.

• Hybrid Zones

  • Over time, two species may further diverge or reconnect, depending on the fitness strength and the reproductive barriers of the hybrids.
  • Over time, the hybrid zone may change depending on the fitness strength and the reproductive barriers of the hybrids .
  • Hybrids can have less fitness, more fitness, or about the same fitness level as the purebred parents.
  • If the hybrids are as fit or more fit than the parents, or the reproductive barriers weaken, the two species may fuse back into one species (reconnection).
  • Discuss how the fitness of a hybrid will lead to changes in the hybrid zone over time

• The Equation of a Line

  • In statistics, linear regression can be used to fit a predictive model to an observed data set of $y$ and $x$ values.
  • Simple linear regression fits a straight line through the set of $n$ points in such a way that makes the sum of squared residuals of the model (that is, vertical distances between the points of the data set and the fitted line) as small as possible.
  • The slope of the fitted line is equal to the correlation between $y$ and $x$ corrected by the ratio of standard deviations of these variables.
  • The intercept of the fitted line is such that it passes through the center of mass $(x, y)$ of the data points.
  • If the goal is prediction, or forecasting, linear regression can be used to fit a predictive model to an observed data set of $y$ and $X$ values.

• The Chi-Square Distribution: Comparison Summary of the Chi-Square Tests Goodness-of-Fit, Independence and Homogeneity

  • Goodness-of-Fit: Use the Goodness-of-Fit Test to decide whether a population with unknown distribution "fits" a known distribution.
  • Goodness-of-Fit is typically used to see if the population is uniform (all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with known distribution.
  • The null and alternative hypotheses are: Ho: The population fits the given distribution.
  • Ha: The population does not fit the given distribution.

• Summary

  • Line of Best Fit or Least Squares Line (LSL): $\hat{y}$= a+bx x = independent variable; y = dependent variable
  • Used to determine whether a line of best fit is good for prediction.
  • Sum of Squared Errors (SSE): The smaller the SSE, the better the original set of points fits the line of best fit.
  • Outlier: A point that does not seem to fit the rest of the data.

• Goodness of Fit

  • The goodness of fit test determines whether the data "fit" a particular distribution or not.
  • Goodness of fit means how well a statistical model fits a set of observations.
  • For example, we may suspect that our unknown data fits a binomial distribution.
  • where $n$ is the number of categories.The goodness-of-fit test is almost always right tailed.
  • These hypotheses hold for all chi-square goodness of fit tests.

• Introduction to fitting a line by least squares regression

  • Fitting linear models by eye is open to criticism since it is based on an individual preference.
  • A scatterplot of the data is shown in Figure 7.12 along with two linear fits.
  • This video covers important ideas and consideration pertaining to fitting a straight line to data.

• Fitting a Curve

  • Curve fitting with a line attempts to draw a line so that it "best fits" all of the data.
  • Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
  • Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data.
  • To find the slope of the line of best fit, calculate in the following steps:
  • Example 1:  Write the least squares fit line and then graph the line that best fits the data:  for $n=8$ points: $(-1,0),(0,0),(1,1),(2,2),(3,1),(4,2.5),(5,3) $ and $(6,4)$.

• Optional Collaborative Classroom Activity

  • Then "by eye" draw a line that appears to "fit" the data.
  • We will plot a regression line that best "fits" the data.
  • It turns out that the line of best fit has the equation:
  • The best fit line always passes through the point .
  • The process of fitting the best fit line is called linear regression.

• Plotting Lines

  • In statistics, charts often include an overlaid mathematical function depicting the best-fit trend of the scattered data.
  • This layer is referred to as a best-fit layer and the graph containing this layer is often referred to as a line graph.
  • It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points; however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:
  • In either case, the best-fit layer can reveal trends in the data.
  • Such curve fitting functionality is often found in graphing software or spreadsheets.