Question

Suppose that you have in your possession bivariate data giving birthrate and life expectancy information for a random sample of 15 countries. For each of the countries, the data give both x, the number of births per one thousand people in the country's population, and y, the country's female life expectancy in years. The least squares regression equation computed from your data is y = 84.06 -0.51x. Suppose that you're predicting the female life expectancy for a country whose birthrate is 39.3 births per one thousand people. You've used the regression equation to make your prediction, and now you're interested in both a prediction interval for this female life expectancy and a confidence interval for the mean female life expectancy for countries with this same birthrate. Suppose that you've computed the following from the data: • mean square error (MSE) - 13.60; 1 (39.3 - x) = 0.1243, where x,..... X denote the birthrates in the sample, and x denotes their mean. I Don't Know Submit ed Tofnery Acces 2019 Meme Educational R

Answer 1

Hi,

1.

The formula for a 95% confidence interval is given by,

ºftw/22n-2 + S. n X-X =2(X; – )

MSE = S = SSE 3 = 13.60

1 x-x O1243 = 0.3526 η Σ.,(α, - 1)2 =

ta/2n-2 = 2.5326

Calculating using this information,

95% confidence interval is given by,

(LCL, UCL) = (36.0071, 42.5929)

2.

The confidence interval would have the same center as, but would be narrower than the prediction interval.

3.

The interval computed from the birthrate of 63.5 would be wider and have a different center.