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