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3. Suppose we obtain a data set for which we are expecting the data points to fit a circle. For the following data sets, obtain the circle of best fit using the equation a(x2 + y2) + bx+cy = 1. a) [4 marks] Let’s start with just four data points: (0,0), (-1,0.5), (-0.5,0.5), (0.3,-0.4). What is the equation of the circle of best fit for this small data set? b) [4 marks] Suppose we now obtain four further data points, for a total of eight data points: (-1,1), (1.3,1), (0.7,0), (-0.8,0.8). What is the equation of the circle of best fit for this enlarged data set? 3. Suppose we obtain a data set for which we are expecting the data points to fit a circle. For the following data sets, obtain the circle of best fit using the equation a(x2 + y2) + bx + cy = 1. a) [4 marks] Let’s start with just four data points: (0,0), (-1,0.5), (-0.5,0.5), (0.3,-0.4). What is the equation of the circle of best fit for this small data set? b) [4 marks] Suppose we now obtain four further data points, for a total of eight data points: (-1,1), (1.3,1), (0.7,0), (-0.8,0.8). What is the equation of the circle of best fit for this enlarged data set? c) [2 marks] For each of the cases (a) and (b) above, plot the data points and the circle of best fit on the same graph (any graphing software is fine!) What do you notice when you compare the two cases? What does this tell you about the risks of drawing conclusions as to the general trends in a data-set when using only a small data sample?
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