1. The data in the table below are given for 9 patients with aplastic anemia.
Table. Hematologic data for patients with aplastic anemia
Patient Lymphocytes
number % Reticulocytes ( per mm2)
1 3.6 1700
2 2.0 3078
3 0.3 1820
4 0.3 2706
5 0.2 2086
6 3.0 2299
7 0.0 676
8 1.0 2088
9 2.2 2013
a. Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y). Interpret the estimated slope.
b. Test for the statistical significance of this regression line using the F test.
c. What is R2 for the regression line? R2 = 0.050
d. What does R2 mean?
e. Test for the statistical significance of the slope using the t test. What do you conclude?
2. The Update to the Task Force Report on Blood Pressure Control in Children reported the observed 90th percentile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in the table below. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task.
Table. 90th percentile of SBP in boys ages 1- 17 of average height
Age (x) SBPa ( y)
1 99
2 102
3 105
4 107
5 108
6 110
7 111
8 112
9 114
10 115
11 117
12 120
13 122
14 125
15 127
16 130
17 132
a. Fit a regression line relating age to SBP, using the data above. Provide the mathematical form of the regression line you obtain and also describe it in lay terms.
b. Provide a 95% confidence interval for the parameters of the regression line.
c. What is the predicted blood pressure for an average 13-year-old boy as estimated from the regression line?
d. What is the standard error of the estimate in c?
e. Answer c and d for a 17-year-old boy.
e. Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer.