Probability with R. Jane M. Horgan

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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 11.1 54.3 20 8.3 32.8 40 8.9 38.5

TABLE 3.2 The Testing Set

Observation Numbers	1	2	3	4	5	6	7	8	9	10
	8.5	9.4	5.4	11.7	6.5	10.3	12.7	11.0	15.4	2.8
	49.4	43.0	19.3	56.4	28.3	53.7	58.1	28.7	80.7	13.6

Use the training set to obtain the line of best fit of on and the testing set to examine how well the line fits the data.

      First, read the training set into R.

      x_train <- c(11.8, 10.8, 8.6, ..., 8.9) y_train <- c(31.3, 59.9, 27.6, ..., 38.5)

      and the testing set

      x_test <- c(8.5, 9.4, 5.4, …, 2.8) y_test <- c(49.4, 43.0, 19.3,…, 13.6)

      Then, plot the training set, to establish if a linear trend exists.

      plot(x_train, y_train, main = "Training Data", font.main = 1)

gives Fig. 3.17.

Figure 3.17 The Scatter of the Training Data

Since Fig. 3.17 shows a linear trend, we obtain the line of best fit of on , and superimpose it on the scatter diagram in Fig. 3.17. In R, write

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