Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 13, Problem 57CR
a.
To determine
Find the expected value of change in biomass concentration associated with a 1-day increase in elapsed time.
b.
To determine
Find the predicted value of biomass concentration if elapsed time is 40 days.
c.
To determine
Check whether there is a linear relationship between the two variables or not.
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A researcher feels that global warming may be reducing average rainfall in Perlis for the past 10 years. The researcher is interested in making predictions for future rainfall. The 10 years data of the
rainfall in Perlis is shown in Table 4.
Table 4
Year
Amount (cm)
2009
40
2010
39
2011
41
2012
29
2013
32
2014
30
2015
15
2016
10
2017
11
2018
20
(a)
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(b)
Predict the rainfall for the year 2019 and 2020.
The article "Earthmoving Productivity Estimation Using Linear Regression Techniques" (S.
Smith, Journal of Construction Engineering and Management, 1999:133–141) presents the
following linear model to predict earth-moving productivity (in m3 moved per hour):
Productivity = - 297.877 + 84.787x, + 36.806x, + 151.680x, – 0.081x, – 110.517x5
- 0.267.x, – 0.016x,x, +0.107.x,x5 + 0.0009448x,x, – 0.244x;x,
where
X1 = number of trucks
X2 = number of buckets per load
X3 = bucket volume, in m³
X4 = haul length, in m
X5 = match factor (ratio of hauling capacity to loading capacity)
X6 = truck travel time, in s
If the bucket volume increases by 1 m², while other independent variables are
unchanged, can you determine the change in the predicted productivity? If so,
determine it. If not, state what other information you would need to determine it.
b. If the haul length increases by 1 m, can you determine the change in the predicted
productivity? If so, determine it. If not, state what other…
The Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the qualification factor):
(image)
a) Find the linear model relating standard time (y) to surface area (x) using linear regression.(x) using linear regression.b) How much time would you allocate to spray painting a new part with a surface area of 250 in2?surface area of 250 in2?c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3), with a surface area of 250 inches2?(study #3), with an area of 150 square inches.d) Perform a significance test of the regression using α= 0.05. Find the P-value for this test.What are your conclusions?e) Estimate the standard errors of the slope and the value of the intercept.f) Calculate the coefficient of determination R2 .g)…
Chapter 13 Solutions
Introduction To Statistics And Data Analysis
Ch. 13.1 - Let x be the size of a house (in square feet) and...Ch. 13.1 - Consider the variables and population regression...Ch. 13.1 - The flow rate in a device used for air quality...Ch. 13.1 - The paper Predicting Yolk Height, Yolk Width,...Ch. 13.1 - A sample of small cars was selected, and the...Ch. 13.1 - Prob. 6ECh. 13.1 - Suppose that a simple linear regression model is...Ch. 13.1 - a. Explain the difference between the line y x...Ch. 13.1 - Prob. 9ECh. 13.1 - Hormone replacement therapy (HRT) is thought to...
Ch. 13.1 - Consider the data and estimated regression line...Ch. 13.1 - A simple linear regression model was used to...Ch. 13.1 - Consider the accompanying data on x = Advertising...Ch. 13.2 - What is the difference between and b? What is the...Ch. 13.2 - The largest commercial fishing enterprise in the...Ch. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - An experiment to study the relationship between x...Ch. 13.2 - The paper The Effects of Split Keyboard Geometry...Ch. 13.2 - The authors of the paper Decreased Brain Volume in...Ch. 13.2 - Do taller adults make more money? The authors of...Ch. 13.2 - Researchers studying pleasant touch sensations...Ch. 13.2 - Prob. 24ECh. 13.2 - Acrylamide is a chemical that is sometimes found...Ch. 13.2 - Prob. 26ECh. 13.2 - Exercise 13.18 described a regression analysis...Ch. 13.2 - Consider the accompanying data on x = Research and...Ch. 13.2 - Prob. 29ECh. 13.2 - In anthropological studies, an important...Ch. 13.3 - The graphs accompanying this exercise are based on...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The article Vital Dimensions in Volume Perception:...Ch. 13.3 - Prob. 35ECh. 13.3 - An investigation of the relationship between x =...Ch. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - In Exercise 13.19, we considered a regression of y...Ch. 13.4 - Prob. 40ECh. 13.4 - A subset of data read from a graph that appeared...Ch. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.4 - The article first introduced in Exercise 13.34 of...Ch. 13.4 - The shelf life of packaged food depends on many...Ch. 13.4 - For the cereal data of the previous exercise, the...Ch. 13.4 - The article Performance Test Conducted for a Gas...Ch. 13.5 - Prob. 48ECh. 13.5 - Prob. 49ECh. 13.5 - A sample of n = 353 college faculty members was...Ch. 13.5 - Prob. 51ECh. 13.5 - Prob. 52ECh. 13.5 - The accompanying summary quantities for x =...Ch. 13.5 - Prob. 54ECh. 13.5 - Prob. 55ECh. 13.6 - Prob. 56ECh. 13 - Prob. 1CRECh. 13 - Prob. 2CRECh. 13 - Prob. 3CRECh. 13 - Prob. 4CRECh. 13 - Prob. 5CRECh. 13 - The accompanying graphical display is similar to...Ch. 13 - Prob. 7CRECh. 13 - Prob. 8CRECh. 13 - Consider the following data on y = Number of songs...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - Prob. 11CRECh. 13 - Prob. 12CRECh. 13 - Prob. 13CRECh. 13 - Prob. 14CRECh. 13 - The discharge of industrial wastewater into rivers...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - It is hypothesized that when homing pigeons are...Ch. 13 - Prob. 18CRECh. 13 - Prob. 57CRCh. 13 - Prob. 58CRCh. 13 - Prob. 59CRCh. 13 - The article Photocharge Effects in Dye Sensitized...Ch. 13 - Prob. 61CRCh. 13 - Prob. 62CRCh. 13 - Prob. 63CRCh. 13 - Prob. 64CRCh. 13 - Prob. 65CRCh. 13 - The article Improving Fermentation Productivity...Ch. 13 - Prob. 67CRCh. 13 - Prob. 68CRCh. 13 - Prob. 69CR
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- The Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the rating factor): (image) To answer:(a) Find the linear model relating standard time (y) to surface area (x) using linear regression. b) How much time would you assign to spray painting a new part with a surface area of 250 in2? c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3) with a surface area of 150 square inches. d) Perform a significance test of the regression using α= 0.05. Find the P-value for this test. What are your conclusions? e) Estimate the standard errors of the slope and the value of the intercept. f) Calculate the coefficient of determination R2 . g) Calculate the correlation coefficient r. Note: The exercise in the image is…arrow_forwardThe Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the rating factor): (image) To answer:(a) Find the linear model relating standard time (y) to surface area (x) using linear regression. b) How much time would you assign to spray painting a new part with a surface area of 250 in2? c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3) with a surface area of 150 square inches. Note: The exercise in the image is the original, it is in Spanish, but it is easy to understand.arrow_forwardA study was done in diesel-powered light-duty pickup truck to see if humidity, air temperature, and barometric pressure influence emission of nitrous oxide (in ppm). Emission measurements were taken at different times, with varying experimental conditions. a. Fit the multiple linear regression model. b. Estimate the amount of nitrous oxide emitted for the conditions where humidity is 50%, temperature is 76 deg F, and barometric pressure is 29.30. Nitrous Humidity, Temp., Pressure. Nitrous Humidity, Temp., Pressure, Oxide, y Oxide, y 0.90 72.4 76.3 29.18 1.07 23.2 76.8 29.38 0.91 41.6 70.3 29.35 0.94 47.4 86.6 29.35 0.96 34.3 77.1 29.2 1.10 31.5 76.9 29.63 0.89 35.1 68.0 29.27 1.10 10.6 86.3 29.56 1.00 10.7 79.0 29.78 1.10 86.0 76.3 11.2 29.48 1.10 12.9 67.4 29.39 0.91 73.3 29.40 1.15 8.3 66.8 29.69 0.87 75.4 77.9 29.28 1.03 20.1 76.9 29.48 0.78 96.6 78.7 29.29 0.77 72.2 77.7 29.09 0.82 107.4 86.8 29.03 1.07 24.0 67.7 29.60 0.95 54.9 70.9 29.37arrow_forward
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