Reference no: EM13957151

The data below present the results of a hydrological investiagtion of the snake river watershed. The main purpose of the investigation was to forecast the water yield (y inches) from april to july using the weighted water content of snow (x), estimated in april 1.

Year	X	Y	Year	X	Y
1919	23.1	10.5	1928	37.9	22.9
1920	32.8	16.7	1929	30.5	14.1
1921	31.8	18.2	1930	25.1	12.9
1922	32.0	17.0	1931	12.4	8.8
1923	30.4	16.3	1932	35.1	17.4
1924	24.0	10.5	1933	31.5	14.9
1925	39.5	23.1	1934	21.1	10.5
1926	24.2	12.4	1935	27.6	16.1
1927	52.2	24.9

Sum x = 511.20

Sum y = 267.20

Sum x^2 = 16597

Sum y^2 = 4554

Sum x*y = 8649.8

From mini tab I get the regression equation to be

C2=0.521C1.

Assuming the relationship between x and y to be approximately linear, use the method of least squares estimation to obtain an appropriate equation for forecasting y which passes through the origin.

Find point estimates and 95% confidence intervals for:

1) the slope of the true regression line of y on x;

2) the standard deviation of the 'error' about this line;

3) the true expected value of y when x=30.0

Also obtain a 95% prediction interval for y when x=30.0