The data below present the results of a hydrological investigation 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 on 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

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

Find point estimates and 95% confidence intervals for:
1) the slope of the true regression line of y on x;
Slope is
B1 = Sum x*y / Sum x^2 = 0.5019
Intercept is
Bo = Ym - B1*Xm = 0.6251

Let e = Y-(Bo +B1*X)
Compute SUM (e^2) = 45.62
Then variance is σ2= SUM (e^2) /(n-2)= 45.62/(17-2)=3.04
variance of B1 ...

Solution Summary

Forecasting and Confidence Intervals are investigated. The solution is detailed and well presented.

Please help with the following problem.
Using the data on the table below, are there any correlations between population changes for the areas listed.
The following is a list of acceptable tests:
regression line and equation; correlation
one-sample t-test
one-sample t confidence interval
matched-pairs t-test
two-sa

Suppose that, for a sample size n = -100 measurements, we find that x = 50. Assuming that the standard deviation equals 2, calculate confidenceintervals for the population mean with the following confidence levels:
a) 95% b) 99% c) 97% d) 80% e) 99.73% f) 92%

1. Why are confidenceintervals useful?
2. You and a colleague conducted a study on grocery totals for shoppers in the State of Michigan. Your estimated grocery totals at CI 95%: ($78, $98). In writing the report, your colleague stated: "There is a 95% chance that the true value of ยต will fall between $78 and $98.
a.

Please answer the following questions:
(a) Explain why a confidence interval for the slope or intercept would be equivalent to a two-tailed hypothesis test.
(b) Why is it especially important to test for a zero slope?

ConfidenceIntervals for the Mean (Large Samples)
Find the critical value zc necessary to form a confidence interval at the given level of confidence. (References: definition for level of confidence
a. 95%=
b. 75%=

1. A computer company wants to study the relationship between the number of microcomputers in use in different areas and the number of software packages the company sells in the areas. A simple linear regression analysis of 21 geographical regions reveals the following: b0=12.43, b1= 1.076, s(b0)=13.65, s(b1)=0.083 , SSE (sum of

I need to modify the data set to show If the time of month has any correlation to the amount of days people are absent. You can skew the numbers one way or another but I need a completed data set. The data set will be used for:
- Calculate coefficient of correlation and coefficient of determination.
- Develop a single linear

Step by step, please show all work.
21) For n = 6 data points, the following quantities have been calculated:
3xy = 400 3x = 40 3y = 76 3x^2 = 346 3y^2 = 1160
(a) Determine the least squares regression line.
(b) Determine the standard error of estimate.
(c) Construct the 95% confidence interval for the mean of y whe

I'm working on linear regressionand I'm stuck on the equation because I'm coming up with a negative number which I don't think is an accurate forecast. The problem also asks for error tests, which I think I have the correct formulas for and will work once the first part is done. Please help! Full details and questions attached