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Regression Analysis for Mthematical Measurements

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).

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Table 1. Measured object values

# Object Diameter Circumference # Object Diameter Circumference
1 Cup 80 251 21 Plate 140 440
2 Mug Small 90 283 22 Hairspray 89 280
3 Mug Large 100 314 23 Weshner 90 283
4 Baby cup 60 188 24 Plastic bottle 70 220
5 Small dip bowl 50 157 25 Disinfectant 92 289
6 Travel cup lid 95 298 26 Perfume 52 163
7 Dessert plate 190 597 27 Tanning oil 30 94
8 Dinner plate 250 785 28 Soup bottle 133 418
9 Salad plate 200 628 29 Mug 120 377
10 Dip bowl 120 377 30 Tums 72 226
11 Febreze 60 188 31 Hydroflask 85 267
12 Advil 50 157 32 Candle 100 314
13 Water bottle 100 314 33 Protein Powder 135 424
14 Sparking bottle 70 220 34 Cup 90 283
15 Mug 140 440 35 Pill bottle 35 110
16 Aloe container 160 503 36 Instant coffee 70 220
17 Perfume 40 126 37 Plate 230 723
18 Sunscreen 30 94 38 Shampoo 55 173
19 Vitamin cont. 110 346 39 Basket 250 785
20 Small bowl 120 377 40 Jar 80 251

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.

Data scatter plot
Figure 1. Data scatter plot

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.

Statistical processing results
Figure 2. Statistical processing results

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).

The linear trend for data with the equation
Figure 3. The linear trend for data with the equation

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.

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