3. Solve for the values of I for graphs showing a direct proportionality between variables. ConclusionDATA ANALYSIS Dhjectivea I To construct and interpret the graphical representation of data ' To determine relationships among variables I To use linear least square ts in analyzing data Concepts A. Preparing lGraphs It is essential when conducting laboratory work to always record and tabulate the data gathered in every measurement It is customary to present this data in a way that can be easily interpreted and analyzed. Constructing graphs is the most conunon tool in data presentation in Physics and other sciences. It is through which that one can have a quick picture of the overall trend of the data. Graphs are commonly constructed using rectangular Cartesian coordinates. These coordinates are any two variables plotted against each other. The horizontal line in a Cartesian plane is the x-axis and the vertical line is the y-axis. Their point of intersection is called the origin. In preparing a graph, choose a proper scale For each of die axis. Remember that it is not necessary to use the same scale for both axes. Use a convenient scale with equally spaced divisions. it is suggested that these divisions are in multiples of 2, 5, or 11'] units. This makes interpolations easier. Graphs should always have scales that are properly labeled. The labels must contain the name and the units of each variable along each axis. Major scale divisions should also be labeled with appropriate numbers. Lastly, in giving a title For each graph, bear in mind that it is a routine to state the vertical axis versus the horizontal axis. Thus, in a position versus time graph, the position vatiable is placed along the vertical axis while the time variable is along the horiZontal axis. All the graphs should be plotted as scattered points and do not attempt to connect the data with a smooth curve. Only when the mathematical form of the data is known that a continuous line representing the overall trend of the data can be drawn. For cases when linearity is assumed, a straight line can be obtained from the linear leastsquares tting method. B. Linear Least Squares In most laboratory experiments, the relationship between the two variables is investigated. It can be done by changing one variable and measuring how the other variable changes as a funcu'on of the rst variable. Most often, it is assumed that there exists a linear relationship between them. If we let these two variables as :r and y. where the former is treated as the independent variable, we can write ,1? = mx + b (1) to show mathematically their relationship. In this equationI m. and h are constants. In a graph, these constants are the slope and the y-intercept of a line, respectively. The simplest and most practical way to confirm whether the data obtained in an experiment obey equation 1 is to graph the data and then draw the best straight line possible through the data points. in this process, the qualitative validation of equation '1 is acquired. This can, however, be veried numerically by linear least-squares tting or linear regression