Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Textbook Question
Chapter 14.4, Problem 61E
This exercise requires use of a statistical software package. The accompanying n = 25 observations on y = Catch at intake (number of fish), x1 = Water temperature (°C), x2 = Minimum tide height (m), x3 = Number of pumps running, x4 = Speed (knots), and x5 = Wind-
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A researcher interested in explaining the level of foreign reserves for the country of
Barbados estimated the following multiple regression model using yearly data
spanning the period 2001 to 2016:
FR=a+BOIL+yEXP+8FDI
Where FR = yearly foreign reserves ($000's), OIL = annual oil prices, EXP =
yearly total exports ($000's) and FDI = annual foreign direct investment ($000's).
The sample of data was processed using MINITAB and the following is an extract
of the output obtained:
Predictor
Сoef
StDev
t-ratio
p-value
Constant
5491.38
2508.81
2.1888
0.0491
OIL
85.39
18.46
4.626
0.0006
EXP
-377.08
112.19
0.0057
FDI
-396.99
160.66
-2.471
**
S = 2.45
R-sq
96.3%
R-sq (adj)
95.3%
Analysis of Variance
Source
DF
MS
F
Regression
1991.31
663.77
??
Error
12
77.4
6.45
Total
15
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values *', ***', '?'and ??'
d) Hence test whether B is significant. Give reasons for your answer.
e) Perform the F…
The administration of a midwestern university commissioned a salary equity study to help establish benchmarks for faculty salaries. The administration utilized the following regression model for annual salary, y : ?(?) β0+β1x ,where ?=0 if lecturer, 1 if assistant professor, 2 if associate professor, and 3 if full professor. The administration wanted to use the model to compare the mean salaries of professors in the different ranks.
a) Explain the flaw in the model.
b)Propose an alternative model that will achieve the administration’s objective.
c) If the global F-test for the model you proposed in 2 is conducted, what would be the value of the numerator degrees of freedom?
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 - Prob. 38ECh. 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...
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardOlympic 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?arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+B01L+YEXP+8FDI Where FR = yearly foreign reserves (So000's), OIL = annual oil prices, EXP = yearly total exports (S000's) and FDI = annual foreign direct investment ($000's). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 s - 2.45 R-sq = 96.3% R-sq(adj) = 95.3% Analysis of Variance Source DF MS F Regression 3 1991.31 663.77 ?? Error 12 43. רר 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values **', **', '?'and *??"arrow_forward
- A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15 Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.arrow_forwardExplain which characteristic of the STA leads to a consideration of a logistic model as opposed to a linear regression mode.arrow_forwardA company randomly samples 48 months of monthly output and monthly total cost data. The sampled data will be used to develop a total cost curve for the company. The company believes that its monthly total cost depends, to a large extent on its monthly output, and hopes that a simple linear regression model will be useful in analyzing how total costs vary as monthly output varies. The company proposes the following model: Total Cost = Fixed Cost + Variable Cost per Unit *Monthly Output. Recall that fixed costs do not vary with the level of monthly output, while the variable cost per unit describes the change in total costs when monthly output changes by one unit. Regression Statistics Standard Error| 64.252 Observations 48 ANOVA df SS MS Regression 1 3097160 3097160 Residual 46 189904 4128 Total 47 3287064 Standard Error Coefficients I Stat Intercept 38.25 24.28 1.6 Monthly Output 19.69 0.72 27.4 A statistician has been asked by the company to conduct a statistical test to determine if…arrow_forward
- A researcher wants to investigate the influence of the average no. of nights spent per year by the tourists from Japan on the average amount spent by them. Table 3 shows the related data obtained from the Department of Statistics Malaysia website. Table 4 shows a portion of Microsoft Excel output for the regression analysis performed based on the data in Table 3. Table 3: Data on the nights spent by tourists from Japan and amount spent Year Average no. of nights spent Average amount spent (in RM billion) 2010 5.9 1.1 2011 6.1 1.1 2012 6.1 1.4 2013 6.3 1.5 2014 6.4 1.8 2015 6.1 1.6 2016 6.2 1.3 2017 6.3 1.2 2018 6.6 1.7 2019 6.9 2.3 Table 4: Regression analysis Coefficients Standard Error t Stat P-value Intercept B0 1.4555 -3.7583 0.0056 Average no. of nights spent B1 0.2312 4.7934 0.0014 a. Note that the value of B0 and B1 are missing from Table 4.…arrow_forwardA b carrow_forwardThe Conde Nast Traveler Gold List for 2012 provided rating for the top 20 small cruise ships. The data from annual Readers’ Choice Survey are the overall scores(Y) each ship received based on several criteria, including Itineraries/Schedule (X1), Shore Excursions(X2), and Food/Dinning(X3). The estimated regression equation to predict the overall scores is Y= 35.6184+0.1105 X1+0.2445 X2+0.2474 X3. Part of the regression results is shown below. Coefficients Standard Error Intercept 35.6184 13.2308 Itineraries/Schedule(X1) 0.1105 0.1297 Shore Excursions(X2) 0.2445 0.0434 Food/Dinning(X3) 0.2474 0.0621 Use the T test to determine whether or not the coefficient of X1 is significant. Use Level of significance=.05? Be sure to state null and alternative hypotheses.…arrow_forward
- Nonearrow_forwardAssume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?arrow_forwardConsider the following data,Study Hours (Y): 2, 4 ,6 ,8 ,10 ,13, 7Sleeping Hours (X): 10, 9, 8, 7,6 ,7, 5 i) Calculate and analyze the fitted regression line between the number of study hours and the number of sleeping hours of different intakes of CSE students.ii) Find the coefficient of determination and interpret your data.iii) Predict study hour when he/she sleeps 11 hours.arrow_forward
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