Item 5
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.
R2 0.519
Std. Error 6.977
n 64
ANOVA table
Source SS df MS F p-value
Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11
Residual 3,018.3339 62 48.6828
Total 6,278.4320 63
Regression output confidence interval
variables coefficients std. error t Stat p-value Lower 95% Upper 95%
Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252
X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563
(a) Write the fitted regression equation.
yˆy^
= + X
(b-1) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (Round t critical value to 3 decimal places.)
Degrees of freedom
tcrit ±
(b-2) Choose the correct option for H0: β1 = 0 vs H1: β1 ≠ 0.
multiple choice 1
• Do not reject the null hypothesis if tcalc > 1.999 Incorrect
• Reject the null hypothesis if tcalc > 1.999
(c-1) Calculate t. (Round your answer to 3 decimal places.)
tcalc
(c-2) We reject the null hypothesis.
multiple choice 2
• Yes Correct
• No
(d-1) Find the 95% confidence interval for slope. (Round your answer to 4 decimal places.)
Confidence interval is from to .
(d-2) The confidence interval does not contain zero, which implies
multiple choice 3
• there is a relationship between the total assets (billions) and total revenue (billions). Correct
• there is no relationship between the total assets (billions) and total revenue (billions).
(e-1) Calculate t2 and F. (Round your answers to the nearest whole number.)
t2
Fcalc
(e-2) Calculate R2.
R2R2
(e-3) What is the percentage of variation in total revenue explained by total assets? (Round your answer to 1 decimal place.)
The percentage of variation in total revenue explained by total assets is %
(f) Increasing assets increases income.
multiple choice 4
• Yes Correct
• No
Item6
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Item 6
Click here for the Excel Data File
Use the standard error to construct an approximate prediction interval for Y using an alpha of 5%. (Round your answer to 3 decimal places.)
Prediction interval for Y:
yˆiy^i
±
Based on the width of this prediction interval, would you say the predictions are good enough to have practical value?
multiple choice
• Yes Correct
• No
rev: 07_18_2019_QC_CS-173384
7
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Item 7
Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
(a) Calculate the t statistic for each slope. From the p-values, which slopes differ from zero at α = .01? (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)
Dependent Variable R2 Estimated Slope Std Error tcalculated p-value Differ from 0?
Highest grade achieved 0.056 -0.033 0.017 .055
Reading grade equivalent 0.164 -0.089 0.020 .000
Class standing 0.056 -0.002 0.019 .916
Absence from school 0.059 3.100 1.710 .072
Grammatical reasoning 0.050 0.112 0.050 .027
Vocabulary 0.115 -0.231 0.039 .000
Hand-eye coordination 0.050 0.024 0.018 .185
Reaction time 0.035 10.800 6.660 .108
Minor antisocial behavior 0.011 -0.406 0.414 .329
(b) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
multiple choice
• Yes Correct
• No
8
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Item 8
Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors’ advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit).
Predictor Coefficient
Intercept 1,263.91
FloorSpace 11.29
CompetingAds −6.889
Price −0.1446
(a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.)
yˆy^
= + * FloorSpace + * CompetingAds + * Price
(b-1) The coefficient of FloorSpace says that each additional square foot of floor space
multiple choice 1
• adds about 11.29 to sales (in thousands of dollars). Correct
• takes away 11.29 from sales (in thousands of dollars).
• takes away 0.1496 from sales (in thousands of dollars).
• adds about 6.889 to sales (in thousands of dollars).
(b-2) The coefficient of CompetingAds says that each additional $1,000 of "competitors' advertising expenditures"
multiple choice 2
• reduces sales by about 6.889 from sales (in thousands of dollars). Correct
• takes away11.29 from sales (in thousands of dollars).
• adds about 6.889 to sales (in thousands of dollars).
• takes away 0.1446 from sales (in thousands of dollars).
(b-3) The coefficient of Price says that each additional $1 of advertised price
multiple choice 3
• reduces sales by about 0.1446 from sales (in thousands of dollars). Correct
• adds about 6.889 to sales (in thousands of dollars).
• takes away 11.29 from sales (in thousands of dollars).
• reduces sales by about 6.889 from sales (in thousands of dollars).
(c) The intercept is not meaningful, since a mountain bike cannot sell for zero, which will happen if all the variables are zero.
multiple choice 4
• True Correct
• False
(d) Make a prediction for Sales when FloorSpace = 84, CompetingAds = 88, and Price = 1,138. (Enter your answer in thousands. Round your answer to 2 decimal places.)
Sales $ thousand
9
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Item 9
Using data set G, answer the questions given below.
DATA SET G Mileage and Vehicle Weight
(n = 73 vehicles)
Vehicle City MPG Weight Vehicle City MPG Weight
Acura CL 20 3,968 Land Rover Range Rover Sport 13 5,137
Audi A5 22 3,583 Lexus IS 250 21 3,461
BMW 4 Series 428i 22 3,470 Lexus LS 460 16 4,233
BMW X1 sDrive28i 23 3,527 Lexus RX 350 18 4,178
Buice LaCrosse 18 3,990 Lincoln MKT 17 4,702
Buick Enclave 17 4,724 Lincoln MKZ 22 3,713
Buick Regal 21 3,692 Lincoln Navigator 14 5,794
Cadillac ATS 22 3,315 Mazda 2 28 2,306
Cadillac CTS 20 3,616 Mazda CX-5 Sport 26 3,194
Cadillac Escalade 14 5,527 Mercedes-Benz C-250 22 3,428
Chevrolet Camaro 1SS 16 3,719 Mercedes-Benz CL600 12 4,894
Chevrolet Cruze LS 26 3,097 Mercedes-Benz ML350 17 4,751
Chevrolet Impala LTZ 19 3,800 Mini-Cooper 29 2,605
Chevrolet Malibu 2LT 25 3,532 Mitsubishi Outlander Sport SE 25 3,296
Chevrolet Spark LS 31 2,269 Nissan Armada SV 13 5,267
Chevrolet Suburban LTZ 15 5,674 Nissan Cube S 25 2,789
Chrysler 200 Touring LX 20 3,402 Nissan Maxima SV 19 3,570
Chrysler 300 S 19 4,029 Nissan Murano SV 18 4,011
Dodge Charger SXT 16 3,996 Nissan Versa S 27 2,363
Dodge Dart Limited 23 3,242 Porsche Cayenne 15 4,398
Fiat 500 Sport 31 2,434 Scion FR-S 25 2,806
Ford Fiesta S 29 2,575 Scion iQ 36 2,127
Ford Focus SE 27 2,960 Scion XD 27 2,665
Ford Mustang GT 15 3,618 Suburu Forester 2.5i Limited 24 3,419
Ford Taurus 19 4,054 Suburu Legacy 2.5i Limited 24 3,427
Honda Accord LX 24 3,192 Toyota Camry XLE 25 3280
Honda CRV LX 23 3,305 Toyota Land Cruiser 13 5,765
Hyundai Azera Limited 19 3,605 Toyota RAV4 XLE 24 3,465
Hyundai Genesis 5.0 15 4,240 Toyota Yaris 30 2,295
Hyundai Santa Fe GLS 18 3,933 Volkswagen Beetle 2.5L 22 3,038
Infiniti Q60 19 3,633 Volkswagen Jetta SE 25 3,070
Infiniti QX50 17 3,790 Volkswagen Toureg V6 Sport 17 4,711
Jaguar F-Type 20 3,477 Volkswagen Passat SE 24 3,230
Jeep Compass Limited 21 3,258 Volvo S60 T5 21 3,528
Jeep Grand Cherokee Limited 17 4,685 Volvo XC90 16 4,667
Kia Forte LX 25 2,776
Kia Soul 24 2,615
Kia Sportage LX 21 3,186
Click here for the Excel Data Set G
Choose the dependent variable (the response variable to be "explained") and the independent variable (the predictor or explanatory variable).
(a-1) Dependent Variable
multiple choice 1
• City MPG Correct
• Weight
(a-2) Independent Variable
multiple choice 2
• Weight Correct
• City MPG
(b) Obtain the regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
Y = X +
(c) Calculate R2. (Round your answer to 4 decimal places.)
R2
(d-1) Zero is contained in the 95% confidence interval.
multiple choice 3
• No Correct
• Yes
(d-2) The slope is different from zero.
multiple choice 4
• Yes Correct
• No
(e) Calculate the degrees of freedom and t-critical for a two-tailed t test for zero slope at α = 5 .05. (Round your answers to 2 decimal places.)
Degrees of freedom
t - critical ±
(f-1) Small p-values tell us the null hypothesis is false.
multiple choice 5
• Yes Correct
• No
(f-2) The sample provides significant evidence that the slope is negative.
multiple choice 6
• Yes Correct
• No
rev: 09_28_2018_QC_CS-140830
10
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Item 10
A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors: LifeExp (life expectancy in years), InfMort (infant mortality rate), Density (population density per square kilometer), GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results.
Regression Analysis–Stepwise Selection (best model of each size)
153 observations
BirthRate is the dependent variable
p-values for the coefficients
Nvar LifeExp InfMort Density GDPCap Literate s Adj R2 R2
1 .0000 6.318 .722 .724
2 .0000 .0000 5.334 .802 .805
3 .0000 .0242 .0000 5.261 .807 .811
4 .5764 .0000 .0311 .0000 5.273 .806 .812
5 .5937 .0000 .6289 .0440 .0000 5.287 .805 .812
Click here for the Excel Data File
(a) Which model (Nvar 1, 2, 3, 4, or 5) best balances fit and parsimony?
The three Correctvariable model best balances fit and parsimony.
(b) Does the addition of LifeExp and Density improve the model with respect to the R2adj?
multiple choice
• Yes
• No Correct
(c) Which two variables appear to be the most significant? (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)
check all that apply
• LifeExpunanswered
• InfMortunanswered
• Densityunanswered
• GDPCapunanswered
• Literate
• 12
• 2points
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• Item 12
• Perform the regression and write the estimated regression equation. Do the coefficient signs agree with you’re a priori expectations? (Round your answers to 4 decimal places.)
Click here for the Excel Data Set A
Mileage and Other Characteristics of Randomly Selected Vehicles (n = 73, k = 4)
Obs Vehicle CityMPG Length Width Weight ManTran
1 Acura TL 20 109.3 74.0 3968 0
2 Audi A5 22 108.3 73.0 3583 1
3 BMW 4 Series 428i 22 182.6 71.9 3470 0
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
71 Volkswagen Passat SE 24 191.6 72.2 3230 0
72 Volvo S60 T5 21 182.2 73.4 3528 0
73 Volvo XC90 16 189.3 76.2 4667 0
•
• yˆy^
• = − length − width − Weight − ManTran
14
2points
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Item 14
Click here for the Excel Data Set C.
Answer the following questions.
(a) Using Data Set C, fill in the missing data. (Round your p-values to 4 decimal places and other answers to 2 decimal places.)
R2
ANOVA table
Source F p-value
Regression
Variables p-value
Intercept
Floor
Offices
Entrances
Age
Freeway
(b) The predictors whose p-values are less than 0.05 are (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)
check all that apply
• Freewayunanswered
• Entranceunanswered
• Floorunanswered
• Ageunanswered
• Officeunanswered
(c) The predictors that were found to have significant coefficients from the t tests are the same ones that are significant from using the p-values.
multiple choice 1
• True
• False
(d) When checking for significance, most prefer the p-value approach because
multiple choice 2
• The p-value actually tells the strength of the significance.
• It is easier than looking up a critical value for the t statistic.
15
2points
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Item 15
A ski resort asked a random sample of guests to rate their satisfaction on various attributes of their visit on a scale of 1–5 with 1 = very unsatisfied and 5 = very satisfied. The estimated regression model was Y = overall satisfaction score, X1 = lift line wait, X2 = amount of ski trail grooming, X3 = safety patrol visibility, and X4 = friendliness of guest services.
Predictor Coefficient
Intercept 2.9018
LiftWait 0.1642
AmountGroomed 0.2343
SkiPatrolVisibility 0.0602
FriendlinessHosts −0.1193
(a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.)
yˆy^
= + * LiftWait + * AmountGroomed + * SkiPatrolVisibility + * FriendlinessHosts
(b) Interpret each coefficient.
Overall satisfaction increases Correctwith an increase in satisfaction for each individual predictor except for friendliness of hosts.
(c) Would the intercept seem to have meaning in this regression?
multiple choice
• Yes
• No Correct
(d) Make a prediction for Overall Satisfaction when a guest’s satisfaction in all four areas is rated a 3. (Round your answer to 4 decimal places.)
Overall satisfaction score
Sample Solution