ŷ = Hematologic data for patients with aplastic anemia Patient number % Reticulocytes Lymphocytes (per mm²) 2 1 3 H₁: 4 5 6 8 9 3.6 2.0 0.3 0.3 0.2 3.0 0.0 1.0 2.2 1,720 3,068 1,840 2,716 2,066 2,289 656 2,108 (a) Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y). (Round your numerical values to four decimal places.) 2,033 (b) What is R2 for the regression line in (a)? (Round your answer to four decimal places.) (c) What does R2 mean in (b)? OR2 indicates the proportion of variation of the percentage of reticulocytes that is explained by lymphocyte OR2 indicates the proportion of variation in lymphocyte count that is explained by the percentage of reticulocytes. (d) Test for the statistical significance of the regression line using the t test. (Use a = 0.05.) State the null and alternative hypotheses. (Enter != for # as needed.) Ho: Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = What can you conclude?
ŷ = Hematologic data for patients with aplastic anemia Patient number % Reticulocytes Lymphocytes (per mm²) 2 1 3 H₁: 4 5 6 8 9 3.6 2.0 0.3 0.3 0.2 3.0 0.0 1.0 2.2 1,720 3,068 1,840 2,716 2,066 2,289 656 2,108 (a) Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y). (Round your numerical values to four decimal places.) 2,033 (b) What is R2 for the regression line in (a)? (Round your answer to four decimal places.) (c) What does R2 mean in (b)? OR2 indicates the proportion of variation of the percentage of reticulocytes that is explained by lymphocyte OR2 indicates the proportion of variation in lymphocyte count that is explained by the percentage of reticulocytes. (d) Test for the statistical significance of the regression line using the t test. (Use a = 0.05.) State the null and alternative hypotheses. (Enter != for # as needed.) Ho: Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value = What can you conclude?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Hematologic Data for Patients with Aplastic Anemia
#### Table: Patient Data
| Patient Number | % Reticulocytes | Lymphocytes (per mm²) |
|----------------|-----------------|-----------------------|
| 1 | 3.6 | 1,720 |
| 2 | 2.0 | 3,068 |
| 3 | 0.3 | 1,840 |
| 4 | 0.3 | 2,716 |
| 5 | 0.2 | 2,066 |
| 6 | 3.0 | 2,289 |
| 7 | 0.0 | 656 |
| 8 | 1.0 | 2,108 |
| 9 | 2.2 | 2,033 |
#### Analysis and Interpretation
**(a)** Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y). (Round your numerical values to four decimal places.)
\[\hat{y} = \text{(Enter equation here)}\]
**(b)** What is \( R^2 \) for the regression line in (a)? (Round your answer to four decimal places.)
\[ R^2 = \text{(Enter value here)}\]
**(c)** What does \( R^2 \) mean in (b)?
- \( R^2 \) indicates the proportion of variation of the percentage of reticulocytes that is explained by lymphocyte count.
- \( R^2 \) indicates the proportion of variation in lymphocyte count that is explained by the percentage of reticulocytes.
**(d)** Test for the statistical significance of the regression line using the t test. (Use \( \alpha = 0.05 \).)
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
- \( H_0: \text{(Enter null hypothesis here)}\)
- \( H_1: \text{(Enter alternative hypothesis here)}\)
Calculate the test statistic. (Round your answer to two decimal places.)
\[ \text{Test Statistic = (Enter value here)} \]
Use technology to find the p-value. (Round your answer to four decimal places.)
\[ p\text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93e02f2d-b0b4-40f2-b59c-ee2919cc5490%2F5e725c3b-ff9e-43aa-8d60-77fe23fd93c1%2Fuii6ytq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hematologic Data for Patients with Aplastic Anemia
#### Table: Patient Data
| Patient Number | % Reticulocytes | Lymphocytes (per mm²) |
|----------------|-----------------|-----------------------|
| 1 | 3.6 | 1,720 |
| 2 | 2.0 | 3,068 |
| 3 | 0.3 | 1,840 |
| 4 | 0.3 | 2,716 |
| 5 | 0.2 | 2,066 |
| 6 | 3.0 | 2,289 |
| 7 | 0.0 | 656 |
| 8 | 1.0 | 2,108 |
| 9 | 2.2 | 2,033 |
#### Analysis and Interpretation
**(a)** Fit a regression line relating the percentage of reticulocytes (x) to the number of lymphocytes (y). (Round your numerical values to four decimal places.)
\[\hat{y} = \text{(Enter equation here)}\]
**(b)** What is \( R^2 \) for the regression line in (a)? (Round your answer to four decimal places.)
\[ R^2 = \text{(Enter value here)}\]
**(c)** What does \( R^2 \) mean in (b)?
- \( R^2 \) indicates the proportion of variation of the percentage of reticulocytes that is explained by lymphocyte count.
- \( R^2 \) indicates the proportion of variation in lymphocyte count that is explained by the percentage of reticulocytes.
**(d)** Test for the statistical significance of the regression line using the t test. (Use \( \alpha = 0.05 \).)
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
- \( H_0: \text{(Enter null hypothesis here)}\)
- \( H_1: \text{(Enter alternative hypothesis here)}\)
Calculate the test statistic. (Round your answer to two decimal places.)
\[ \text{Test Statistic = (Enter value here)} \]
Use technology to find the p-value. (Round your answer to four decimal places.)
\[ p\text
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