Question: The data in the following table show the age at onset, X, for patients diagnosed with a certain disease, and the number of years, Y, that they survived after onset.
|
Onset X
|
Survival Y
|
|
Onset X
|
Survival Y
|
|
15
|
10.9
|
|
37
|
4.4
|
|
25
|
13.9
|
|
37
|
5.8
|
|
27
|
9.2
|
|
39
|
6.0
|
|
29
|
12.8
|
|
40
|
5.2
|
|
29
|
12.0
|
|
42
|
5.5
|
|
29
|
9.6
|
|
48
|
3.0
|
|
32
|
12.2
|
|
59
|
3.8
|
|
35
|
8.8
|
|
|
|
Σxi = 523 Σyi = 123.1 Σxi2 = 19759 Σyi2 = 1192.67 Σxiyi = 3874
(a) Calculate the mean age at onset and mean survival period for these patients.
(b) Calculate the intercept and slope for the fitted line Y= b0 + b1.x. (You may use Minitab) Interpret the meaning of the slope in words. Does the intercept have a practical interpretation for these data?
(c) Calculate a 95% confidence interval for the true slope b1. (You may use Minitab). Use your interval to test the hypothesis that survival time is not linearly related to age at onset. What do you conclude?
(d) Calculate the correlation between X and Y. Also calculate the R2. Interpret this figure.
(e) Calculate Yˆand a 90% confidence interval for mean Y when X=40.
(f) Suppose a person has just been diagnosed with this disease and it is ascertained that onset occurred at age 40. Give a 90% prediction interval for their future life expectancy.