5 1. Consider the regression mode, y = a + ßx+ɛ; where, E (ɛ | x) = 0, E(ɛx) = 0, Var (ɛ|x)= oʻ,and Var [(a+ ßx)|x] = 0.(a) Derive Var(y|x).(b) The errors are homoscedastic [i.e, Var (ɛ\x)= o²] in this case. Based on the given regressionequation, show that, Var(y|x) < Var (y).

Answered: Consider the regression mode, y = a +…

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.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 48CR

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The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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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.

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Consider the regression mode, y = a + Bx + ɛ; where, E (ɛ | x) = 0, E(ɛx) = 0, Var (ɛ|x)= oʻ, and Var [(a + Bx)|x] = 0. (a) Derive Var(y|x).