Group 3 Chapter 1 Objectives PresentationDiagram various types of graphs and graphing techniques.Discuss curve fitting techniques. Explain the function of the chi-square test and interpretation of results. :Group 3 Chapter 1 Objectives PresentationDiagram various types of graphs and graphing techniques.Discuss curve fitting techniques. Explain the function of the chi-square test and interpretation of results. Lesha MullinBen WeismanJose Nunex


Diagram various types of graphs and graphing techniques. :Diagram various types of graphs and graphing techniques. Graphs are a visual way to convey large amounts of information. Graphs are used to predict one variable based on another. One variable is often said to depend on another independent variable. Nuclear Medicine commonly uses linear line graphs using an x axis and a y axis.


-Diagram various types of graphs and graphing techniques. :-Diagram various types of graphs and graphing techniques.


Diagram various types of graphs and graphing techniques. :Diagram various types of graphs and graphing techniques. A straight line graph of y Versus x is represented by the Formula y= a + bx The y intercept in the value of Y at x=0, is represented by a. The slope, which represents the Steepness of the line is Represented by b.


Diagram various types of graphs and graphing techniques. :Diagram various types of graphs and graphing techniques. The slope is calculated From any two arbitrary Points on the line as: Slope= Y= (Y2 – Y1) X (X2 – X1) This slope is calculated from the Points (X1, Y1)=(0, 5) and (X2, Y2)=(10, 10) Slope = (10-5)= 0.5 (10-0)


Diagram various types of graphs and graphing techniques. :Diagram various types of graphs and graphing techniques. Questions Q1: When would you use a connect-the-dots type line? A: An example of when you might use a connect-the-dots line would be on a graph of the number of kidney scans performed monthly. Q2: What does the sign of the slope represent? A: Reflects whether the curve of the graph slopes upward (positive slope) or downward (negative slope.) Q3: Why are straight line curves used in Nuclear Medicine? A: to prove a direct or linear relationship between two variables or to predict some y variable based on the value of the x variable.


Diagram various types of graphs and graphing techniques. :Diagram various types of graphs and graphing techniques. Questions Q4: How do you transform date into a straight line for exponential curves such as radioactive decay? A: We take the natural logarithm of the activity. Q5: Why is the straight line preferred? A: Because subsequent interpretations or calculations are simplified. References Nuclear Medicine and PET – Technology and Techniques Fifth Edition


Objective :Objective Discuss curve fitting techniques


What is curve fitting? :What is curve fitting? It is a mathematical representation on an xy Cartesian graphing plane which describes the relationship between variables x & y


Slide 10:The relationships can show a linear function


Slide 11:The relationship can be non-linear


The Least Squares Method :The Least Squares Method In this process, the squared distances from each data point to the line that best represents the line or curve are summated. The most accurate way to determine the parameters of a line that best represent all data points in a set. AKA linear regression


Questions :Questions An engineer has measured the force exerted by a spring as a function of its displacement from its equilibrium position. The following data have been obtained: Data Point # Distance(cm) Force (N) 1 2 2 2 4 3.5 3 7 4.5 4 11 8.0 5 17 9.5 #1) Plot this set of data on an xy plane #2) Draw a line that best represents these points #3) Is the relationship linear or nonlinear


Slide 15:The following data have been obtained for voltage in across a battery capacitor Time (s) Voltage 0 10 1 6.06 3 2.23 5 0.82 7 0.30 9 0.11 #4) Plot this data set #5) Is it linear or nonlinear.


References :References Christian, Paul E. (2004) Nuclear Medicine and PET: Technology and Techniques. United States: Mosby, Inc. pgs 18-20. Curvefit.com (1999). The difference between linear and nonlinear regression. Retrieved August 31, 2006, from: http://www.libs.uga.edu/ref/apastyle.html


Slide 18:Chi-square Test The Chi-square law (x2) test is used to determine an acceptable range of variability in the repeat measurements. (C=EC/n), and X2 is calculated as: X^2=[E(C – C)^2]/C