In this laboratory work, the linear regression model is investigated as applied to the measured results of diameters and lengths of circles of forty different objects. The report is group work; each student has made ten measurements independently, which reduces the unambiguous and subjectivity of the obtained data. The first step in preparing the report is to make a table reflecting all measured results of diameters and lengths of circles in millimeters and indicate to which object the characteristics belong (Table 1).
Table 1. Measured object values
Since the table has been compiled, it is necessary to start drawing the data scattering graph. For this purpose, the text table is entered into an Excel spreadsheet, and a chart is drawn, as shown in Figure 1.
The third stage of results processing is using the linear regression model to obtain the correlation coefficient of the sample, significance test, and regression line calculation. This action is performed by using the regression function embedded in the program that makes data analysis. The statistical processing results are shown in Figure 2: as can be seen, the model reliability (R2) is high, so one can confidently speak about the results’ reliability. The correlation coefficient between the two variables (D. and C.) is 0.999998863, which indicates an incredibly strong correlation. This does not seem surprising since the results of the circle lengths directly depend on the diameter of the round object. Moreover, if the opposite result were obtained, indicating a low correlation, one would have to look for an error in measurement or processing. The outcome of the test for significance is presented in column F, which shows 16704669.09.
To construct the equation of linear regression, it is necessary to complete the linear trend on the already available chart and apply the function expression (Figure 3).
In general, the linear regression test reasonably accurately reflects the correlation of data on simple models that are not prone to oscillations. If it were to measure financial performance, currency rates, or stock prices, the linear regression model would only be an auxiliary tool. Therefore, it is worth noting that one should be careful when using this tool for statistical analysis. Among the unique findings, the incredibly low “significance F” score should be noted, which allows rejecting the null hypothesis. This project helped to recall the theory concerning the linear regression model.