Given: The following points (all units are feet): Easting Northing 0.00 9.98 60.

Question

Given: The following points (all units are feet):

Easting Northing

0.00 9.98

60.00 10.18

260.00 10.22

460.00 10.13

660.00 9.87

860.00 9.75

1060.00 10.02

1259.24 9.98

Using the least squares regression analysis find the best fit line for the above data. You know that a monumnet needs to be placed at an Easting of 1324.76feet. The northing that the monument needs to be placed at is _______________________. (two decimal places).

The bearing of the best fit line is ____________________________ (in DDMM'SS" format).

Explanation / Answer

To calculate The least square regression line we require x, xy ,y , x2  

Here, these values are calculated in the given table is

Here the least square regression line is

y^ = a + bx

where a =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [80.13 * 4167285 - 4619.24 * 46015.42] / [8 * 4167285 - 4619.242 ]

a = 10.1133

b =  [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [8 * 46015.42 - 4619.24 * 80.13] / [  8 * 4167285 - 4619.242 ]

b = -0.000168

so y^ = 10.1133 - 0.000168x

so at easting = 1324.76 feet

y^ = 10.1133 - 0.000168 * 1324.76 = 9.89 feet

Here the bearing is the angle = tan-1 [0.000168] = 34.65''

Easting (X) Northing (Y) x^2 xy 0 9.98 0 0 60 10.18 3600 610.8 260 10.22 67600 2657.2 460 10.13 211600 4659.8 660 9.87 435600 6514.2 860 9.75 739600 8385 1060 10.02 1123600 10621.2 1259.24 9.98 1585685 12567.22 Sum 4619.24 80.13 4167285 46015.42

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