Q3: An investigator has reported the data tabulated below for an experiment to determine the growth rate of bacteria k (per d), as a function of oxygen concentration c (mg/L). It is known that such data can be modeled by the following equation: 1 1 Cs 1 k kmax' kmax c2 and kmax where c, and kmax are parameters. Use linear regression to estimate and predict the growth rate at c = 2 mg/L. Cs 0.5 0.8 1.5 2.5 4 k 1.1 2.4 5.3 7.6 8.9 Note: y = ao + a1. x 1 y k 1 ao kmax Cs a1 kmax X = c2 II II II

Q3: An investigator has reported the data tabulated below for an experiment to determine the growth rate of bacteria k (per d), as a function of oxygen concentration c (mg/L). It is known that such data can be modeled by the following equation: 1 1 Cs 1 k kmax' kmax c2 and kmax where c, and kmax are parameters. Use linear regression to estimate and predict the growth rate at c = 2 mg/L. Cs 0.5 0.8 1.5 2.5 4 k 1.1 2.4 5.3 7.6 8.9 Note: y = ao + a1. x 1 y k 1 ao kmax Cs a1 kmax X = c2 II II II

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.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

See similar textbooks

Similar questions

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
Does Table 1 represent a linear function? If so, finda linear equation that models the data.
If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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.
Can the average rate of change of a function be constant?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Determine whether the trend appears linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.
Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.
Run a simple linear regression in SPSS to know if previous experience (‘prevexp’: Previous Experience-months) significantly predicts current salary(‘salary’: Current Salary) in the work force . Use α =.05 Interpret each of the terms of the regression equation That is, interpret: X, Ŷ, a and b
Consider the multiple regression model to investigate the relationship between the number of fishes (Y) per section of the stream and the following independent variables: dissolved oxygen (3 < oxy < 10, in mg/liter), maximum depth (1 < maxdepth < 8, in feet), and water temperature (5< temp < 20, in °C). The location of the stream was also considered (lowland and upland). Y-hat = 23.09 + 0.199*oxy + 0.3361*maxdepth +8.6730*temp + 3.8290* lowland. Which of the following is(are) TRUE about the estimated regression coefficient for location of the stream? 1. The location of the stream is a categorical variable, so it is represented by a dummy variable with upland stream as the reference variable. II. Holding other factors constant, the number of fishes in lowland is 3.8290 higher than upland streams. O A. I only O B. II only O C. Both I and II O D. Neither I nor II
Researchers studying the association between (x)the number of daily hours of intense artificial lightand (y) the rate of plant growth (cm/month) foundsx = 1.5, sy = 3.0, and r = 0.80. The regression modelthey created predicts growth of 5 cm/month with 2 hoursof this light per day. What’s the predicted growth rate for3 hours of artificial light daily?A) 5.4 cm/moB) 5.8 cm/moC) 6.6 cm/moD) 7.0 cm/moE) 7.8 cm/mo