EBK FUNCTIONS AND CHANGE: A MODELING AP
6th Edition
ISBN: 8220103600101
Author: Crauder
Publisher: CENGAGE L
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Chapter 5.4, Problem 8E
To determine
(a)
To find:
The correction effect that correction factor have on energy loss due to respiration if the temperature is larger than
To determine
(b)
To find:
The correction effect that correction factor have on energy loss due to respiration if the temperature is exactly
To determine
(c)
To find:
The correction effect that correction factor have on energy loss due to respiration if the temperature is less than
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Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
Σx = 476, Σy = 87.1, Σx2 = 62,290, Σy2 = 2046.87, Σxy = 11121.3,and r ≈ 0.94367.
x days 72 76 32 91 205y km/100 14.7 19.6 5.3 11.7 35.8
a) Use a 1% level of significance to test the claim ? > 0.(Use 2 decimal places.)t =critical t=
b) Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2 decimal places.)________ km/100
c) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)lower limit = _____…
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the
Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of
recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
x days
y km/100
74
75
34
92
203
14.9
19.5
5.4
11.9
35.8
(a) Verify that Ex = 478, Ey = 87.5, Ex2 - 61,930, Ey? = 2054.67, Exy = 11110.9, and r- 0.94201.
Ex
£y
Ex?
Ey²[
Exy
(b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.)
critical t
Conclusion
O Reject the null hypothesis, there is sufficient evidence that p > 0.
O Reject the null hypothesis, there is insufficient evidence that p > 0.
Fail to reject the null hypothesis, there is insufficient evidence that p > 0.…
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands.
Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study
ocean currents.
x days
y km/100
71
76
31
92
203
14.2
19.6
5.8
11.2
35.9
(a) Verify that Ex = 473, Ey = 86.7, Ex² = 61,451, Ey?
2033.69, Exy = 10995.7, and r 0.93868.
%3D
%3D
%3D
%3D
%3D
Σχ
Ey
Ex?
Ey2
Σχy
(b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.)
critical t
Conclusion
Reject the null hypothesis, there is sufficient evidence that p > 0.
Reject the null hypothesis, there is insufficient evidence that p > 0.
O Fail to reject the null hypothesis, there is insufficient evidence…
Chapter 5 Solutions
EBK FUNCTIONS AND CHANGE: A MODELING AP
Ch. 5.1 - TEST YOUR UNDERSTANDING Another fish population...Ch. 5.1 - Prob. 2TUCh. 5.1 - Prob. 3TUCh. 5.1 - Special Rounding instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...
Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Prob. 11ECh. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Prob. 13ECh. 5.1 - Long-Term Data and the Carrying Capacity This is a...Ch. 5.1 - Prob. 15ECh. 5.1 - Cable TV The following table shows the number C....Ch. 5.1 - World Population The following table shows world...Ch. 5.1 - Prob. 18ECh. 5.1 - More on the Pacific Sardine This is a continuation...Ch. 5.1 - Modeling Human Height with a Logistic Function A...Ch. 5.1 - Eastern Pacific Yellowfin Tuna Studies to fit a...Ch. 5.1 - Prob. 22ECh. 5.1 - Special Rounding Instructions When you perform...Ch. 5.1 - Prob. 24ECh. 5.1 - SKILL BUILDING EXERCISES Estimating Optimum Yield...Ch. 5.1 - SKILL BUILDING EXERCISES Estimating Carrying...Ch. 5.1 - SKILL BUILDING EXERCISES Logistic GrowthWhen we...Ch. 5.1 - SKILL BUILDING EXERCISES Percentage Rate of Change...Ch. 5.1 - SKILL BUILDING EXERCISES HarvestingWhat is the...Ch. 5.1 - SKILL BUILDING EXERCISES Harvesting Suppose a...Ch. 5.1 - SKILL BUILDING EXERCISES Harvesting Continued The...Ch. 5.1 - SKILL BUILDING EXERCISES Finding Logistic...Ch. 5.1 - Prob. 9SBECh. 5.1 - Prob. 10SBECh. 5.1 - Prob. 11SBECh. 5.1 - Prob. 12SBECh. 5.1 - Prob. 13SBECh. 5.1 - Prob. 14SBECh. 5.1 - Prob. 15SBECh. 5.1 - Prob. 16SBECh. 5.1 - Prob. 17SBECh. 5.1 - Prob. 18SBECh. 5.1 - Prob. 19SBECh. 5.1 - Prob. 20SBECh. 5.1 - Prob. 21SBECh. 5.1 - Prob. 22SBECh. 5.1 - Prob. 23SBECh. 5.1 - Prob. 24SBECh. 5.1 - Prob. 25SBECh. 5.1 - Prob. 26SBECh. 5.1 - Prob. 27SBECh. 5.1 - Prob. 28SBECh. 5.1 - Prob. 29SBECh. 5.1 - Prob. 30SBECh. 5.1 - Prob. 31SBECh. 5.1 - Prob. 32SBECh. 5.1 - Prob. 33SBECh. 5.1 - Prob. 34SBECh. 5.1 - Prob. 35SBECh. 5.1 - Prob. 36SBECh. 5.1 - Prob. 37SBECh. 5.2 - TEST YOUR UNDERSTANDING In the situation of the...Ch. 5.2 - Prob. 2TUCh. 5.2 - Prob. 3TUCh. 5.2 - Prob. 1ECh. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Prob. 4ECh. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Prob. 15ECh. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Tsunami Waves and BreakwatersThis is a...Ch. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Reminder Round all answers to two decimal places...Ch. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 1SBECh. 5.2 - Prob. 2SBECh. 5.2 - Prob. 3SBECh. 5.2 - Prob. 4SBECh. 5.2 - Prob. 5SBECh. 5.2 - Prob. 6SBECh. 5.2 - HomogeneityExercises S-7 through S-I3 deal with...Ch. 5.2 - Homogeneity Exercises S-7 through S-13 deal with...Ch. 5.2 - HomogeneityExercises S-7 through S-I3 deal with...Ch. 5.2 - Prob. 10SBECh. 5.2 - Prob. 11SBECh. 5.2 - Homogeneity Exercises S-7 through S-13 deal with...Ch. 5.2 - Prob. 13SBECh. 5.2 - Prob. 14SBECh. 5.2 - Prob. 15SBECh. 5.2 - Prob. 16SBECh. 5.2 - Making Power FormulasIn Exercises S-16 through...Ch. 5.2 - Prob. 18SBECh. 5.2 - Making Power FormulasIn Exercises S-16 through...Ch. 5.2 - Prob. 20SBECh. 5.3 - Prob. 1TUCh. 5.3 - Prob. 2TUCh. 5.3 - Prob. 3TUCh. 5.3 - Zipfs Law The following table shows U.S cities by...Ch. 5.3 - Planetary Velocity The following table gives the...Ch. 5.3 - Stopping Distance The table below shows the...Ch. 5.3 - Distance to the Horizon A sailor records the...Ch. 5.3 - Hydroplaning On wet roads, under certain...Ch. 5.3 - Urban Travel Times Population of cities and...Ch. 5.3 - Mass-Luminosity Relation Roughly 90 of all stars...Ch. 5.3 - Growth Rate Versus Weight Ecologists have studied...Ch. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Reminder Round all answers to two decimal places...Ch. 5.3 - Prob. 19ECh. 5.3 - Weight Versus Height The following data show the...Ch. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 1SBECh. 5.3 - Prob. 2SBECh. 5.3 - Prob. 3SBECh. 5.3 - Prob. 4SBECh. 5.3 - An Easy Power Formula Model the following data...Ch. 5.3 - Prob. 6SBECh. 5.3 - Prob. 7SBECh. 5.3 - Prob. 8SBECh. 5.3 - Prob. 9SBECh. 5.3 - Prob. 10SBECh. 5.3 - Prob. 11SBECh. 5.3 - Prob. 12SBECh. 5.3 - Prob. 13SBECh. 5.3 - Prob. 14SBECh. 5.3 - Prob. 15SBECh. 5.3 - Prob. 16SBECh. 5.3 - Prob. 17SBECh. 5.4 - TEST YOUR UNDERSTANDING | FOR EXAMPLE 5.10 When...Ch. 5.4 - Prob. 2TUCh. 5.4 - TEST YOUR UNDERSTANDING | FOR EXAMPLE 5.12 Find a...Ch. 5.4 - Prob. 4TUCh. 5.4 - EXERCISES Reminder Round all answers to two...Ch. 5.4 - Round all answers to two decimal places unless...Ch. 5.4 - EXERCISE River flow The cross sectional area C, in...Ch. 5.4 - EXERCISES Net Profit Margin The net profit margin...Ch. 5.4 - A Skydiver If a skydiver jumps from an airplane,...Ch. 5.4 - Present Value If you invest P dollars the present...Ch. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Reminder Round all answers to two decimal places...Ch. 5.4 - Reminder Round all answers to two decimal places...Ch. 5.4 - Average Traffic Spacing The headway h is the...Ch. 5.4 - Prob. 13ECh. 5.4 - Decay of Litter Litter such as leaves falls to the...Ch. 5.4 - Prob. 15ECh. 5.4 - Reminder Round all answers to two decimal places...Ch. 5.4 - Reminder Round all answers to two decimal places...Ch. 5.4 - Prob. 18ECh. 5.4 - Reminder Round all answers to two decimal places...Ch. 5.4 - Prob. 20ECh. 5.4 - SKILL BUILDING EXERCISES Formula for Composed...Ch. 5.4 - SKILL BUILDING EXERCISES Formula for Composed...Ch. 5.4 - SKILL BUILDING EXERCISES Formulas for Composed...Ch. 5.4 - SKILL BUILDING EXERCISES Formula for Composed...Ch. 5.4 - Formulas for Composed functions In Exercises S-5...Ch. 5.4 - Formulas for Composed functions In Exercises S-5...Ch. 5.4 - Formulas for Composed functions In Exercises S-5...Ch. 5.4 - Formulas for Composed functions In Exercises S-5...Ch. 5.4 - Limiting values Find the limiting value of...Ch. 5.4 - Multiplying Functions A certain function f is the...Ch. 5.4 - Adding Functions A certain function f is the sum...Ch. 5.4 - Decomposing Functions Let f(x)=x2 and g(x)=x+1....Ch. 5.4 - Decomposing Functions If f(x)=x2+3, express f as a...Ch. 5.4 - Prob. 14SBECh. 5.4 - Decomposing Functions To join a book club, you pay...Ch. 5.4 - Prob. 16SBECh. 5.4 - Combining Functions Let f(x)=x21 and g(x)=1x. Find...Ch. 5.5 - TEST FOR UNDERSTANDING FOR EXAMPLE 5.14 Find a...Ch. 5.5 - TEST YOUR UNDERSTANDINGFOR EXAMPLE 5.15 What range...Ch. 5.5 - TEST FOR UNDERSTANDING FOR EXAMPLE 5.16 In the...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - 5.5 EXERCISES Reminder Round all answers to two...Ch. 5.5 - Reminder Round all answers to two decimal places...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all answers to two decimal places...Ch. 5.5 - Prob. 12ECh. 5.5 - Reminder Round all the answers to two decimal...Ch. 5.5 - Reminder Round all answers to two decimal places...Ch. 5.5 - Reminder Round all answers to two decimal places...Ch. 5.5 - Prob. 16ECh. 5.5 - 5.5 SKILL BUILDING EXERCISES Using the Quadratic...Ch. 5.5 - 5.5 SKILL BUILDING EXERCISES Using the Quadratic...Ch. 5.5 - 5.5 SKILL BUILDING EXERCISES Using the Quadratic...Ch. 5.5 - 5.5 SKILL BUILDING EXERCISES Using the Quadratic...Ch. 5.5 - 5.5 SKILL BUILDING EXERCISES Using the Quadratic...Ch. 5.5 - Prob. 6SBECh. 5.5 - The Single-Graph method In Exercises S-7 through...Ch. 5.5 - Prob. 8SBECh. 5.5 - Prob. 9SBECh. 5.5 - Prob. 10SBECh. 5.5 - Prob. 11SBECh. 5.5 - Prob. 12SBECh. 5.5 - Prob. 13SBECh. 5.5 - Prob. 14SBECh. 5.5 - Prob. 15SBECh. 5.5 - Prob. 16SBECh. 5.5 - Prob. 17SBECh. 5.5 - Prob. 18SBECh. 5.5 - Prob. 19SBECh. 5.5 - Using Quadratic Regression In Exercises S-13...Ch. 5.6 - The following fictitious table shows kryptonite...Ch. 5.6 - According to Doyle log rule, the length L in feet,...Ch. 5.6 - Prob. 3TUCh. 5.6 - A Dubious Model of Oil Prices The following table...Ch. 5.6 - Speed of Sound in the North Atlantic The speed of...Ch. 5.6 - Traffic Accidents The following table shows the...Ch. 5.6 - Poiseuilles Law for Rate of Fluid Flow Poiseuilles...Ch. 5.6 - Population Genetics In the study of population...Ch. 5.6 - Population Genetics-First Cousins This is a...Ch. 5.6 - Builders old measurement was instituted by law in...Ch. 5.6 - Change in London Travel Time This exercise is a...Ch. 5.6 - An Epidemic Model A certain disease is contracted...Ch. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - C of these fish caught by fishing over the life...Ch. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - 13. Inventory The yearly inventory expense E, in...Ch. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Cubic Regression In Exercise S-1 through S-7, use...Ch. 5.6 - Cubic Regression In Exercise S-1 through S-7, use...Ch. 5.6 - Cubic Regression In Exercise S-1 through S-7, use...Ch. 5.6 - Prob. 4SBECh. 5.6 - Prob. 5SBECh. 5.6 - Cubic Regression In Exercise S-1 through S-7, use...Ch. 5.6 - Prob. 7SBECh. 5.6 - Prob. 8SBECh. 5.6 - Prob. 9SBECh. 5.6 - Prob. 10SBECh. 5.6 - Prob. 11SBECh. 5.6 - Prob. 12SBECh. 5.6 - Prob. 13SBECh. 5.6 - Quartic Regression In Exercise S-8 through S-14,...Ch. 5.6 - Recognizing Polynomials In Exercise S-15 through...Ch. 5.6 - Recognizing Polynomials In Exercise S-15 through...Ch. 5.6 - Recognizing Polynomials In Exercise S-15 through...Ch. 5.6 - Recognizing Polynomials In Exercise S-15 through...Ch. 5.6 - Rational Function Is y=xx1+x a rational function?Ch. 5.6 - S-20 Rational Function Is y=x3+4x2+x+1 is a...Ch. 5.6 - Rational Function? Is y=x+1x2 is a rational...Ch. 5.6 - Finding Poles Find the poles of y=xx23x+2.Ch. 5.6 - Finding Poles Find the poles of y=x+1x2+7x.Ch. 5.6 - Horizontal Asymptotes Find all the horizontal...Ch. 5.6 - Horizontal Asymptotes Find all the horizontal...Ch. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Prob. 16CRCh. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.CR - Prob. 20CRCh. 5.CR - Reminder Round all answers to two decimal places...Ch. 5.FR1 - Prob. 1ECh. 5.FR1 - Prob. 2ECh. 5.FR1 - Prob. 3ECh. 5.FR1 - Prob. 4ECh. 5.FR1 - Prob. 5ECh. 5.FR1 - Prob. 6ECh. 5.FR1 - Prob. 7ECh. 5.FR1 - Prob. 8ECh. 5.FR2 - Prob. 1ECh. 5.FR2 - Prob. 2ECh. 5.FR2 - Prob. 3ECh. 5.FR2 - Prob. 4ECh. 5.FR2 - Prob. 5ECh. 5.FR2 - Prob. 6ECh. 5.FR2 - Prob. 7ECh. 5.FR2 - Prob. 8ECh. 5.FR2 - Prob. 9ECh. 5.FR2 - Prob. 10ECh. 5.FR2 - Prob. 11ECh. 5.FR2 - Prob. 12ECh. 5.FR2 - Prob. 13ECh. 5.FR2 - Reminder Round all answers to two decimal places...Ch. 5.FR2 - Prob. 15E
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- 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.arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days y km/100 72 14.7 203 35.6 76 32 5.3 94 19.5 11.7 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey? = 2028.68, Exy = 11036.6, and r= 0.93853. Ex 477 Ey 86.8 Ex2 62029 Ey2 2028.68 Exy 11036.6 r 0.93853 (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) t 8.15 critical t 4.54 Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p> 0. O Fail to reject the null…arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days y km/100 71 76 31 92 203 14.2 19.6 5.8 11.2 35.9 (a) Verify that Ex = 473, Ey = 86.7, Ex = 61,451, Ey = 2033.69, Exy = 10995.7, and r 0.93868. %3D %3D %3D %3D Σχ 1 473 ΣΥ| 86.7 Ex2 61451 Ey2 2033.69 Exy 10995.7 r0.93868 (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) t 4.72 critical t 4.54 Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject…arrow_forward
- A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) 0.5 -0.5 0 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 9 4 4 5 8 13 14 17 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 6.512 + 5.472 BMI change 20 S 5.26270 R-Sq 27.16% R-Sq (adj) 19.88% 15- : 10- -0.5 0.0 1.5 Ⓡ S 5.26270 Coefficients Term Coef VIF SE Coef 2.26 T-Value 2.88 P-Value 0.0164 Constant 6.512 BMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change = 6.512 + 5.472 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to…arrow_forwardA paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m2) 0.7 0.8 1 1.5 1.2 1 0.4 0.4 0.5 -0.5 0.1 Depression Score Change -1 | 4 5 8 13 14| 17| 18| 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 6.512 + 5.472 BMI change 5.26270 20 - R-Sq R-Sq (adj) 19.88% 27.16% 15- 10-. 5- -0.5 0.0 0.5 1.0 1.5 BMI change 5.26270 27.166 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.512 2.26 2.88 0.0164 BMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change = 6.512 + 5.472 EMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?…arrow_forwardA paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) -0.5 0.7 0.5 0.1 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 4 4 8 13 14 16 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 6.598 + 5.327 BMI change 20- 5.10254 R-Sq R-Sq (adj) 20.06% 27.32% 15- 10- 5- 0- -0.5 0.0 0.5 1.0 1.5 BMI change R-sq 5.10254 27.32% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.598 2.19 3.01 0.0132 BMI change 5.327 2.75 1.94 0.0812 1.00 Regression Equation Depression score change = 6.598 + 5.327 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?…arrow_forward
- When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table: Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07 Let xx represent the flow rate variable and yy represent the variable for soil eroded. Then \bar x = 1.73, s_x = 1.38, \bar y = 2.81, s_y = 1.99xˉ=1.73,sx=1.38,yˉ=2.81,sy=1.99 Use this to complete the following calculation of the correlation coefficient for these data. r = \frac{1}{n-1}\left[\left(\frac{x_1 - \bar x}{s_x}\right)\left(\frac{y_1 - \bar y}{s_y}\right) + \left(\frac{x_2 - \bar x}{s_x}\right)\left(\frac{y_2 - \bar y}{s_y}\right) + \cdots + \left(\frac{x_n - \bar x}{s_x}\right)\left(\frac{y_n - \bar y}{s_y}\right)\right]r=n−11[(sxx1−xˉ)(syy1−yˉ)+(sxx2−xˉ)(syy2−yˉ)+⋯+(sxxn−xˉ)(syyn−yˉ)]…arrow_forwardQuestion 6 For children between the ages of 18 months and 29 months, there is approximately a linear relationship between height and age. The relationship can be represented by ŷ = 62.05 + 0.62x where y represents height (in centimeters) and x represents age (in months). Joseph is 24.5 months old and is 80 centimeters tall. What is Joseph's residual? a) O-31.650 b) O 2.760 c) O 3.760 d) O 111.650 e) O 77.240 f) O None of the abovearrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 75 79 35 91 203 y km/100 14.2 19.1 5.8 11.2 35.4 (a) Verify that Σx = 483, Σy = 85.7, Σx2 = 62,581, Σy2 = 1978.69, Σxy = 10982.3, and r ≈ 0.94895. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t (c) Verify that Se ≈ 4.1118, a ≈ 0.7378, and b ≈ 0.1698. Se a barrow_forward
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