Page 280 - Artificial Intellegence_v2.0_Class_11
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2
              Step 2:     Sum x, y, x  and xy:
                          N = No. of samples = 10


                                           x              y              x 2            xy
                                            2             44              4             88

                                            9             98             81            882

                                            5             80             25            400

                                            3             75              9            225

                                            7             70             49            490

                                            1             63              1             63
                                            8             53             64            424

                                            6             92             36            552

                                           2.5            71           6.25          177.5

                                            4             65             16            260

                                                                        2
                                          ∑x=48         ∑y=711        ∑x =291      ∑xy=3562
              Step 3:     Calculate Slope m:
                                                          m = N Σ(xy) − Σx Σy
                                                                 N Σ(x ) − (Σx) 2
                                                                   2
                                                  =     10(3562) – (48) (711)
                                                       10 (291) – (48) 2

                                                  =     35620 – 34128
                                                        2910 – 2304


                                                  =     1492  = 2.46
                                                       606


              Step 4:     Calculate Intercept b:
                                                            b = Σy − m Σx
                                                                  N
                                                  =     711 – 2.46 (48)
                                                                  1  0

                                                  =     711 – 118.08
                                                             10

                                                  =592.92 = 59.29 = 59.3
                                                      10

              Step 5:     Assemble the equation of a line:
                                                  y = mx + b
                                                  y = 2.46x + 59.3
              Using this equation, we can calculate predicted values of y using any values of x. Let us plot this line on the graph.

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