PLEASE SHOW ALL WORK FOR NUMBER 1, 2, AND 3! Consider the following 15 pairs of

Question

PLEASE SHOW ALL WORK FOR NUMBER 1, 2, AND 3!

Consider the following 15 pairs of x y data points. Graphing these we have reason to believe that there is a linear relationship between the y values and the x values. Use the method of least squares to determine this relationship. Fill in the table below (sigma x_n^2) a + (sigma x_n)_b = (sigma x_n y_n) (sigma x_n) a + (sigma 1) b = (sigma y_n) For this specific problem above these two equations become: ________ _________ Solving these two equations for a and b. a = ___________ b = _____________

Explanation / Answer

1)

2) 506a+66b=396

66a+11b=309

3)a =5.009

b=-1.9636

Total x 1 2 3 4 5 6 7 8 9 10 11 66 y 3 8 14 17 24 27 34 37 44 47 54 309 xy 3 16 42 68 120 162 238 296 396 470 594 2405 xx 1 4 9 16 25 36 49 64 81 100 121 506

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