WEBASSIGN ACCESS FOR PROBABILITY & STATS
9th Edition
ISBN: 9780357893111
Author: DEVORE
Publisher: CENGAGE L
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Chapter 12.3, Problem 42E
Verify that if each xi is multiplied by a positive constant c and each yi is multiplied by another positive constant d, the t statistic for testing H0: β1 = 0 versus Ha: β1 ≠ 0 is unchanged in value (the value of
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Some people don't gain weight even when they overeat. Perhaps fidgeting and other “nonexercise activity"
(NEA) explains why – the body might spontaneously increase nonexercise activity when fed more. Researchers
deliberately overfed 16 healthy young adults for 8 weeks. They measured fat gain (y, in kilograms) and increase
in energy use (NEA) (x, in calories), as an explanatory variable, from activity other than deliberated exercise –
fidgeting, daily living, and the like. Here are the data (sorted by NEA):
NEA increase
-94
-57
-29 135
143
151
245 355
620 690
Fat gain
4.2
3.0
3.7 2.7
3.2
3.6
2.4
1.3
2.3
1.1
Assume that the model Fat gain= Bo +B,NEA increase +ɛ is reasonable. Selected SAS output are given here.
0.73985 R-Square 0.6061
2.38750 Adj R-Sq 0.5780
Root MSE
Dependent Mean
Coeff Var
30.98860
Parameter Estimates
Variable
DF
Parameter Estimate
Standard Error
t Value
Pr > It|
Intercept
1
3.50512
0.30362
11.54
<.0001
1
-0.00344
0.00074141
-4.64
0.0004
nea
(a) Find the average fat…
A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (x), measured in Data for 21 companies who use the bank's services were used to fit the model
E(y) = β0 + β1x.
The results of the simple linear regression are provided below. = 2,700 + 20xInterpret the estimate of β0, the y-intercept of the line.
For every $1 million increase in sales revenue, we expect a service charge to increase $2,700.
All companies will be charged at least $2,700 by the bank.
There is no practical interpretation since a sales revenue of $0 is a nonsensical value.
About 95% of the observed service charges fall within $2,700 of the least squares line.
Tom has been gathering data concerning the cost of a spa treatment, y', during the
before Valentine's Day. The only independent variable that he has considered
is the number of minutes, "x," in the treatment. Suppose Tom collects data on the
relationship between the number of minutes in a treatment and the resulting cost of
we
the treatment. Tom finds that the correlation between cost and number of minutes is
strong and positive. Therefore, he has performed a linear regression analysis on his
data. His results are that the constant "a" is 35, and the coefficient "b1" for the
independent variable is 1.3. Which of the following is the correct linear regression
equation that would allow Tom to predict the cost of a spa treatment given the
number of minutes?
Oy = 78x + 35
Oy' = 1.3x + 35
%3D
Oy = 78x - 1.3
%3D
OY = -1.3x - 35
Chapter 12 Solutions
WEBASSIGN ACCESS FOR PROBABILITY & STATS
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Ch. 12.1 - Suppose that in a certain chemical process the...Ch. 12.2 - Refer back to the data in Exercise 4, in which y =...Ch. 12.2 - The accompanying data on y = ammonium...Ch. 12.2 - Refer to the lank temperature-efficiency ratio...Ch. 12.2 - Values of modulus of elasticity (MOE, the ratio of...Ch. 12.2 - The article Characterization of Highway Runoff in...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - The following data is representative of that...Ch. 12.2 - The bond behavior of reinforcing bars is an...Ch. 12.2 - Wrinkle recovery angle and tensile strength are...Ch. 12.2 - Calcium phosphate cement is gaining increasing...Ch. 12.2 - a. Obtain SSE for the data in Exercise 19 from the...Ch. 12.2 - The invasive diatom species Didymosphenia geminata...Ch. 12.2 - Prob. 25ECh. 12.2 - Show that the point of averages (x,y) lies on the...Ch. 12.2 - Prob. 27ECh. 12.2 - a. Consider the data in Exercise 20. Suppose that...Ch. 12.2 - Consider the following three data sets, in which...Ch. 12.3 - Reconsider the situation described in Exercise 7,...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - Exercise 16 of Section 12.2 gave data on x =...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - For the past decade, rubber powder has been used...Ch. 12.3 - Refer back to the data in Exercise 4, in which y =...Ch. 12.3 - Misi (airborne droplets or aerosols) is generated...Ch. 12.3 - Prob. 37ECh. 12.3 - Refer to the data on x = liberation rate and y =...Ch. 12.3 - Carry out the model utility test using the ANOVA...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Verify that if each xi is multiplied by a positive...Ch. 12.3 - Prob. 43ECh. 12.4 - Fitting the simple linear regression model to the...Ch. 12.4 - Reconsider the filtration ratemoisture content...Ch. 12.4 - Astringency is the quality in a wine that makes...Ch. 12.4 - The simple linear regression model provides a very...Ch. 12.4 - Prob. 48ECh. 12.4 - You are told that a 95% CI for expected lead...Ch. 12.4 - Prob. 50ECh. 12.4 - Refer to Example 12.12 in which x = test track...Ch. 12.4 - Plasma etching is essential to the fine-line...Ch. 12.4 - Consider the following four intervals based on the...Ch. 12.4 - The height of a patient is useful for a variety of...Ch. 12.4 - Prob. 55ECh. 12.4 - The article Bone Density and Insertion Torque as...Ch. 12.5 - The article Behavioural Effects of Mobile...Ch. 12.5 - The Turbine Oil Oxidation Test (TOST) and the...Ch. 12.5 - Toughness and fibrousness of asparagus are major...Ch. 12.5 - Head movement evaluations are important because...Ch. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - The accompanying data on x = UV transparency index...Ch. 12.5 - Torsion during hip external rotation and extension...Ch. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12 - The appraisal of a warehouse can appear...Ch. 12 - Prob. 69SECh. 12 - Forensic scientists are often interested in making...Ch. 12 - Phenolic compounds are found in the effluents of...Ch. 12 - The SAS output at the bottom of this page is based...Ch. 12 - The presence of hard alloy carbides in high...Ch. 12 - The accompanying data was read from a scatterplot...Ch. 12 - An investigation was carried out to study the...Ch. 12 - Prob. 76SECh. 12 - Open water oil spills can wreak terrible...Ch. 12 - In Section 12.4, we presented a formula for...Ch. 12 - Show that SSE=Syy1Sxy, which gives an alternative...Ch. 12 - Suppose that x and y are positive variables and...Ch. 12 - Let sx and sy denote the sample standard...Ch. 12 - Verify that the t statistic for testing H0: 1 = 0...Ch. 12 - Use the formula for computing SSE to verify that...Ch. 12 - In biofiltration of wastewater, air discharged...Ch. 12 - Normal hatchery processes in aquaculture...Ch. 12 - Prob. 86SECh. 12 - Prob. 87SE
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