In a relationship between two variables, one variable is

an independent variable (input variable) and the other one is a dependent

variable (output variable). The value of the dependent variable depends on the

value of the independent variable. On a graph, the independent variable is

shown on the x-axis, while the dependent variable is shown on the y-axis.

A relation between two variables can be linear or

non-linear. The graph of a linear relationship is a straight line and the graph

of a non-linear relationship is a curve. A non-linear relationship can be linearized

using regression analysis to get a line of best fit. The line of best fit can

be used to extrapolate the given data set. The graph of a straight line is based

on its slope and y-intercept. Slope is a measure of steepness of a line () and the y-intercept is the point at

which a graph crosses the y-axis.

The main purpose of most experiments is to derive

meaningful data. Often it is difficult to see the significance in the tabulated

data when the numbers are displayed in a table. By graphing the data sets that

are given, one will notice that it is much easier to see the relationships

between the numbers. The simplest relationship of recorded data occurs when the

independent (x-variable) and dependent (y-variable) variables share a linear

relation. 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 the

origin of the graph. However, not all data can be assumed as a direct relation.

For instance, relationships such as logarithmic, inverse, or a combination of

the two can be used in order to derive the linear relation instead.

The purpose of this lab is to complete two exercises that

require graphing of data sets and using those specific data sets to interpret

which relationships between the variables produce the most linear line. When

calculating the equation of the line, the regression analysis is important to

know because it is used to determine the strength of linearity. If the

regression value is close to 1, the data is strongly related, or in other words

linear. 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 the

trendline, figure 1 illustrated that it was not linear, however seemed very

close to a linear relationship. Figure 2 demonstrated to have a linear

relationship with a trendline reading 3E8 x 7E-11 and a coefficient of determination

coming out to be 1. This justifies that the regression line perfectly fit the

given data that was provided. Using the equation from figure 2, I plugged in

the given frequency of 1/s for

‘x’ to calculate the wavelength of the red color. The wavelength of the red color came

out to be 6.504E-7. Figure 3 looked as if it was almost linear, but it was not

close enough to validate.

In exercise 2, one is expected to graph a total of four

graphs, two of which are temperature vs. volume, with figure 4 in Celsius and

figure 6 in Kelvin. The other two graphs are temperature vs. , with figure 5 in Celsius and figure

7 in Kelvin. Both figures 4 and 6 showed a linear relationship, with equations

y =1.2167x-272.15 and y = 1.2167x+0.8535. From those two equations, one is able

to distinguish that both figures 4 and 6 share the same slope because both

graphs had the temperature vs. volume relationship and 1 degree Kelvin is 273

degrees larger than 1 degree Celsius consistently throughout the graph. This

indication is also confirmed by simply looking at the graph. By looking at

figures 5 and 7, one can realize that temperature vs. was not linear.