In a relationship between two variables, one variable isan independent variable (input variable) and the other one is a dependentvariable (output variable). The value of the dependent variable depends on thevalue of the independent variable. On a graph, the independent variable isshown on the x-axis, while the dependent variable is shown on the y-axis.
A relation between two variables can be linear ornon-linear. The graph of a linear relationship is a straight line and the graphof a non-linear relationship is a curve. A non-linear relationship can be linearizedusing regression analysis to get a line of best fit.
The line of best fit canbe used to extrapolate the given data set. The graph of a straight line is basedon its slope and y-intercept. Slope is a measure of steepness of a line () and the y-intercept is the point atwhich a graph crosses the y-axis. The main purpose of most experiments is to derivemeaningful data. Often it is difficult to see the significance in the tabulateddata when the numbers are displayed in a table. By graphing the data sets thatare given, one will notice that it is much easier to see the relationshipsbetween the numbers. The simplest relationship of recorded data occurs when theindependent (x-variable) and dependent (y-variable) variables share a linearrelation.
The linear numbers are displayed on the graph as a straight line; thus,revealing the x and y-axis relationship as: (where m is the slope and b is the y-intercept).The coefficient b is only represented when the line doesn’t pass through theorigin of the graph. However, not all data can be assumed as a direct relation.For instance, relationships such as logarithmic, inverse, or a combination ofthe two can be used in order to derive the linear relation instead. The purpose of this lab is to complete two exercises thatrequire graphing of data sets and using those specific data sets to interpretwhich relationships between the variables produce the most linear line.
Whencalculating the equation of the line, the regression analysis is important toknow because it is used to determine the strength of linearity. If theregression value is close to 1, the data is strongly related, or in other wordslinear. On the other hand, if the regression coefficient value is close to 0,then the data has little or no relation. Results/Discussion:In exercise 1, one is expected to graph wavelength vs.frequency (figure 1), wavelength vs. (figure 2) and log of wavelength vs.
frequency (figure 3). Based on thetrendline, figure 1 illustrated that it was not linear, however seemed veryclose to a linear relationship. Figure 2 demonstrated to have a linearrelationship with a trendline reading 3E8 x 7E-11 and a coefficient of determinationcoming out to be 1. This justifies that the regression line perfectly fit thegiven data that was provided.
Using the equation from figure 2, I plugged inthe given frequency of 1/s for’x’ to calculate the wavelength of the red color. The wavelength of the red color cameout to be 6.504E-7. Figure 3 looked as if it was almost linear, but it was notclose enough to validate. In exercise 2, one is expected to graph a total of fourgraphs, two of which are temperature vs.
volume, with figure 4 in Celsius andfigure 6 in Kelvin. The other two graphs are temperature vs. , with figure 5 in Celsius and figure7 in Kelvin. Both figures 4 and 6 showed a linear relationship, with equationsy =1.
2167x-272.15 and y = 1.2167x+0.8535.
From those two equations, one is ableto distinguish that both figures 4 and 6 share the same slope because bothgraphs had the temperature vs. volume relationship and 1 degree Kelvin is 273degrees larger than 1 degree Celsius consistently throughout the graph. Thisindication is also confirmed by simply looking at the graph. By looking atfigures 5 and 7, one can realize that temperature vs. was not linear.