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?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
You want to look at an ANOVA table of a regression in which a dependent variable is predicted using an intercept and one slope coefficient. Unfortunately, as you want to look at the table, you knock over your coffee mug which smudges out some of the numbers. Here is what you still can read: • n=7 • F-ratio = 15 • Residual sum of squares (RSS) = 16 • t-score of the slope coefficient = 3.873 How big is the explained sum of squares (ESS)? a 44 b 52 c 48 d 40 How big is the total sum of squares (TSS)? a 64 b 52 c 60 d 56 How big is the explained R-squared? a 0.7 b 0.75 c 0.8 d Cannot be determined What's the p-value for the F-ratio? a 0.012 b 0.024 c 0.036 d…
What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Coefficient Std Error т P Constant -2298.36 158.531 -14.50 0.0000 Size 11598.9 230.111 50.41 0.0000 Resid. Mean Square (MSE) R-Squared Adjusted R-Squared 0.8925 1248950 0.8922 Standard Deviation 1117.56 Interpret the coefficient of determination for the regression model. A) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values. B) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. C) There is sufficient evidence to indicate that the size of the diamond is a useful predictor of the price of a diamond when testing at alpha =…
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What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Interpret the standard deviation of the regression model. a) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values. b) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model. c) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. d) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
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