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Finding the Line of Best Fit
                 A child’s age and height are recorded for study. Let’s find the line of best fit.
                                                        Age(years)    Height (cms)
                                                             0             20
                                                             1             40
                                                             2             60
                                                             3             80
                                                             4             92
                                                             5            105
                 Let us find the best m (slope) and b (y-intercept) that suits the data.
                 y = mx + b
                                                         2
                 Step 1:  For each (x,y), we have to calculate x  and xy as shown in the table below:
                                              x              y             x 2            xy
                                              0             20              0              0
                                              1             40              1             40
                                              2             60              4            120
                                              3             80              9            240
                                              4             92             16            368
                                              5            105             25            525

                                                                                                 2
                                                                    2
                 Step 2:  We have to add all the elements present in x, y, x  and xy (which gives us Σx, Σy, Σx  and Σxy):
                                              x              y             x 2            xy
                                              0             20              0              0
                                              1             40              1             40
                                              2             60              4            120
                                              3             80              9            240
                                              4             92             16            368
                                              5            105             25            525
                                            ∑x=15         ∑y=397         ∑x =55        ∑xy=1293
                                                                           2
                                  N = no. of data samples = 6
                 Step 3:  Now we will calculate the slope m:
                                                           m = N Σ(xy) – Σx Σy
                                                                    2
                                                                   N Σ(x ) – (Σx) 2
                                                       6(1293) – 15(397)
                                                     =
                                                         6(55) – (15) 2
                                                       7758 – 5955
                                                     =  330 – 225

                                                       1803
                                                     =
                                                       105
                                                     = 17.17

                 Step 4:  After calculating the slope now we need to calculate the intercept b:
                                                              b = Σy – m Σx
                                                                       N
                                                              397 – 17.17 (15)
                                                            =
                                                                     6
                                                                                                 Maths for AI   187
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