In: Statistics and Probability
The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126.
Redshift |
0.02380.0238 |
0.05410.0541 |
0.07230.0723 |
0.03960.0396 |
0.04420.0442 |
0.01090.0109 |
|
---|---|---|---|---|---|---|---|
Distance |
0.340.34 |
0.730.73 |
0.990.99 |
0.560.56 |
0.620.62 |
0.140.14 |
a. Find the explained variation.
(Round to six decimal places as needed.)
b. Find the unexplained variation.
(Round to six decimal places as needed.)
c. Find the indicated prediction interval.
billion
light-yearsless than<yless than<nothing
billion light-years