MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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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Step 1: Determine the given information
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Step 2: Determine the regression line y on x
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Step 3: Determine the coefficient of determination (R2) and its interpretation
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Step 4: Determine the test for statistical significance for regression line using t-test.
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