One method of assessing avalanche risk involves relating angles x and y by a straight line through the origin, of the form y = ßx. Here x represents the angle between the starting zone of the avalanche and the horizontal at a point where the mountain profile has a slope of 10°, and y represents the angle between the starting zone and the horizontal at the avalanche limit. starting zone X 10° local angle is 10° y avalanche limit Ten avalanches gave the following values for x and y: mountain profile 8 9 10 avalanche 1 2 3 4 5 6 7 x()20 20 25 25 25 30 30 35 35 40 y (0) 15 18 22 23 23 25 29 23 32 32 10 (a) By minimising the residual sum of squares (y - 3x)2 with derive an expression for the least squares estimate in terms of Xi (b) Estimate from the data given above. (c) If x= 20°, what is your predicted value for y? respect to 3, and yi.

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