Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 14.3, Problem 45E
a.
To determine
Test whether the chosen model is useful or not at 0.05 level of significance.
b.
To determine
Check whether the interaction term is important or not.
c.
To determine
Explain whether the model utility test indicates a useful model.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a
regression analysis was performed, and a portion of the computer output is as follows:
ŷ
= 4.3 14.9x
Coefficients
(Intercept)
X
Estimate St
4.3
Ho: B₁ = 0
Ha: B₁ > 0
B1
O Ho: B₁
Ha: B₁ <0
= 0
14.9
B1
O Ho: B₁ = 0
0
Ha: B1
Std. Error Test statistic P-value
2.9
5.1
1.48
Specify the null and the alternative hypotheses that you would use in order to test whether a negative
linear relationship exists between x and y.
2.92
0.08
0.01
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
y = Retail PRICE (measured in dollars)
X1 = Microprocessor SPEED (measured in megahertz)
(Values in sample range from 10 to 40)
x 2 = CHIP size (measured in computer processing units)
(Values in sample range from 286 to 486)
A first-order regression model. was fit to the data. Part of the printout follows:
Parameter Estimates
T FOR 0
ERROR PARAMETER = 0 PROB>ITI
PARAMETER STANDARD
VARIABLE DF
ESTIMATE
INTERCEPT 1
-373.526392
1258.1243396 -0.297
0.7676
SPEED
1
104.838940
22.36298195 4 688
0.0001
сHP
1
3.571850
3.89422935
0.917
0.3629
Identify and interpret the estimate of B2-
3. Wine Participant magazine has collected average price per bottle for the prestigious Chateau Le Thundebird bordeaux for different vintages (years).
The data appears in the table below.
year of bottling
price
a) draw the scatter diagram showing how wine price varies by vintage year
b) use the most appropriate regression equation to determine the relationship
between year of bottling (age) and price.
c) what is the explanatory power (RSQ) of that equation
d) determine the predicted price of a bottle of this wine for the 2017 vintage.
2009
36
2010
40
2011
51
2012
60
2013
68
2014
72
2015
70
2016
65
2018
51
2019
44
2020
39
Chapter 14 Solutions
Introduction To Statistics And Data Analysis
Ch. 14.1 - Prob. 1ECh. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - The relationship between yield of maize (a type of...
Ch. 14.1 - Prob. 11ECh. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28ECh. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - When Coastal power stations take in large amounts...Ch. 14.3 - Prob. 39ECh. 14.3 - The article first introduced in Exercise 14.28 of...Ch. 14.3 - Data from a random sample of 107 students taking a...Ch. 14.3 - Benevolence payments are monies collected by a...Ch. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62ECh. 14 - Prob. 63CRCh. 14 - Prob. 64CRCh. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CRCh. 14 - Prob. 68CRCh. 14 - Prob. 69CRCh. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CRCh. 14 - Prob. 72CRCh. 14 - This exercise requires the use of a statistical...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardIf 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?arrow_forwardThe 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 19.02arrow_forward
- 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.arrow_forwardDoes Table 1 represent a linear function? If so, finda linear equation that models the data.arrow_forwardRetail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) x1= Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model was fit to the data. Part of the printout follows: Analysis of Variance SOURCE DF MS F VALUE PROB>F MODEL 2 34593103.008 17296051,504 19.018 0.0001 ERROR 57 51840202.926 909477.24431 C TOTAL 59 86432305.933 ROOT MSE 953.66516 3197.96667 R-SQUARE 0.4002 0.3792 DEP MEAN CV. ADJ R-SQ 29.82099 Test to determine if the model is adequate for predicting the price of a computer. Use a = .01.arrow_forward
- The authors of the paper "Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickness, Egg Surface Area of Japanese Quails Using Various Egg Traits as Regressors"t used a multiple regression model with two independent variables where y = quail egg weight (g), X, = egg width (mm), and X2 = egg length (mm). The regression function suggested in the paper is -21.658 + 0.828x, 0.373x2. + (a) What is the mean egg weight for quail eggs that have a width of 20 mm and a length of 48 mm? (Enter your answer to three decimal places.) (b) Interpret the value of B,. O When width is fixed, the mean increase in weight associated with a 1-mm increase in length is 0.373 g. When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.373 g. O When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.828 g. O When width is fixed, the mean increase in weight associated with a 1-mm increase…arrow_forwardThe accompanying Minitab regression output is based on data that appeared in the article "Application of Design of Experiments for Modeling Surface Roughness in Ultrasonic Vibration Turning."+ The response variable is surface roughness (um), and the independent variables are vibration amplitude (um), depth of cut (mm), feed rate (mm/rev), and cutting speed (m/min), respectively. The regression equation is Ra = -0.972 - 0.0312a + 0.557d + 18.3f + 0.00282v Predictor Coef SE Coef Constant -0.9723 0.3923 -2.48 0.015 -0.03117 0.01864 -1.67 0.099 d 0.5568 0.3185 1.75 0.084 18.2602 0.7536 24.23 0.000 0.002822 0.003977 0.71 0.480 S = 0.822059 Source R-Sq = 88.6 R-Sq (adj) = 88.04 DS MS 0.000 Regression Residual Error 4 401.02 100.25 148.35 76 51.36 0.68 Total 80 452.38 (a) How many observations were there in the data set? observations (b) Interpret the coefficient of multiple determination. O 8.0% of the observed variation in feed rate can be explained by the model relationship with vibration…arrow_forwardThe quality of the orange juice produced by a certain manufacturer is constantly monitored. Data collected on the sweetness index of an orange juice sample and amount of water-soluble pectin for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x). Find and interpret the coefficient of determination, r2, and the coefficient of correlation, r. Find and interpret the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The coefficient of determination, r2, is enter your response here. Sample variations in the amount of water-soluble pectin explain 100r2% of the sample variation in the sweetness index using the least squares line. B. The coefficient of determination, r2, is enter your…arrow_forward
- The relationship between yield of maize, date of planting, and planting density was investigated in an article. Let the variables be defined as follows. y = percent maize yield x = planting date (days after April 20) z = planting density (plants/ha) The following regression model with both quadratic terms where x₁ = x, X₂ = Z, X3 = x² and x4 = 2² provides a good description of the relationship between y and the independent variables. y =a +B₁x₁ + B₂X₂ + B3X3+B₁x₁ + e (a) If a = 21.07, B₁ = 0.653, B₂ = 0.0022, B3 = -0.0207, and B4 = 0.00002, what is the population regression function? y = 509 X (b) Use the regression function in Part (a) to determine the mean yield for a plot planted on May 7 with a density of 41,182 plants/ha. (Give the exact answer.) (c) Would the mean yield be higher for a planting date of May 7 or May 23 (for the same density)? The mean yield would be higher for [May 7 You may need to use the appropriate table in Appendix A to answer this question.arrow_forwardA doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good cholesterol). He randomly selected 9 of his patients and determined their HDL cholesterol. The data is reported in the table below: a) Compute the regression equation for HDL as a function of age. b)Interpret the meaning of the regression parameters.arrow_forward) A real estate magazine reported the results of a regression analysis designed to predict theprice (y), measured in dollars, of residential properties recently sold in a northern Virginiasubdivision. One independent variable used to predict sale price is GLA, gross living area(x), measured in square feet. Data for 157 properties were used to fit the model,? = β0 + β1x.The results of the simple linear regression are provided below.y = 96,600 +22.5x s = 6500 r2 = -0.77 t = 6.1 (for testing β1)Interpret the estimate of β0 the y-intercept of the line.a. About 95% of the observed sale prices fall within $96,600 of the least squares line.b. There is no practical interpretation, since a gross living area of 0 is a nonsensicalvalue.c. All residential properties in Virginia will sell for at least $96,600.d. For every 1-sq ft. increase in GLA, we expect a property's sale price to increase$96,600.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY