Probability with R. Jane M. Horgan

href="#fb3_img_img_1d5524f8-0129-580f-b9a1-6a417959714b.png" alt="images"/> from . The line of best fit, , is obtained by choosing the intercept and slope so that the sum of the squared distances from the observed to the estimated is minimized. The algebraic details of the derivations of and are given in Appendix B.

      Often, the data for supervised learning are randomly divided into two parts, one for training and the other for testing. In machine learning, we derive the line of best fit from the training set

      The testing set is used to see how well the line actually fits. Usually, an breakdown of the data is made, the 80% is used for “training,” that is, to obtain the line, and the 20% is used to decide if the line really fits the data, and to ascertain if the model is appropriate for future predictions. The model is updated as new data become available.

      Example 3.1

Suppose there are 50 pairs of observations available for obtaining the line that best fits the data in order to predict from . The data are randomly divided into the training set and testing set, using 40 observations for training (Table 3.1), and 10 for testing (Table 3.2).

TABLE 3.1 The Training Set

Observation Numbers			Observation Numbers
1	11.8	31.3	21	15.1	80.1
2	10.8	59.9	22	14.7	66.9
3	8.6	27.6	23	10.5	42.0
4	10.3	57.7	24	10.9	72.9
5	8.5	50.2	25	11.6	67.8
6	11.6	52.1	26	9.1	45.3
7	14.4	79.1	27	5.4	30.2
8	8.6	32.3	28	8.8	49.6
9	12.4	58.8	29	11.2	44.3
10	14.9	79.5	30	7.4	46.1
11	8.9	57.0	31	7.9	45.1
12	8.7	35.1	32	12.2	46.5
13	11.7	68.2	33	8.5	42.7
14	11.4	60.1	34	9.3	56.3
15	8.8	44.5	35	10.0	27.4
16	5.9	28.9	36	3.8	20.2
17	13.5	75.8	37	14.9	68.5
18	8.7	48.7	38	12.4	72.6
19	11.0	54.7	39