Linear Fitting Data and Variables

Study Notes

Variables are sets of observed data influencing one another during experiments.
Axes represent changes in a Cartesian plane used to track relationships between variables.
The X-axis typically indicates the independent variable, while the Y-axis represents the dependent variable.

Independent Variables: Not influenced by other variables; plotted on the abscissa (X-axis).
Explanatory Variables: Affect the outcome of dependent variables and can be multiple.
Dependent Variables: Plotted on the ordinate (Y-axis); their variation depends on independent variables.
Response Variables: Answer research questions and are influenced by explanatory variables.
Categorical Variables: Represented by symbols on coordinate systems.
Lurking Variables: Hidden variables affecting the relationships being studied.

Time Series Graphs: Show changes in the Y-axis as time progresses on the X-axis.
Scatter Plots: Illustrate relationships between two variables and their variance.
Histograms: Display frequency distribution of a variable across specified intervals.

Accuracy: Indicates how close measurements are to the true value.
Precision: Relates to the consistency of repeated measurements.
Uncertainty: Potential errors stemming from measurement limits, user skill, irregularities, and situational factors.

Absolute Uncertainties: Defined by the least significant figure; e.g., 13.21 m ± 0.01.
Fractional Uncertainties: Calculated as uncertainty divided by the measured value; e.g., for 1.2 s ± 0.1, fractional uncertainty = 0.1 / 1.2 = 0.0625.
Percentage Uncertainties: Express fractional uncertainties as a percentage; e.g., percentage uncertainty = (0.1 / 1.2) x 100 = 6.25%.

Errors result from miscalculations or judgment lapses during experiments, affecting result credibility.
Random Errors: Caused by environmental variations or measurement techniques, leading to scattered data values that vary in magnitude and direction.