Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 14, Problem 64CR
a.
To determine
Test whether the model is useful or not.
b.
To determine
Calculate the value of adjusted
c.
To determine
Test whether variable
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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?
You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. What is the critical value of the test statistic (tc) if you want to perform a test for the significance of a single right-hand side (explanatory) variable at α = 0.05?
a.) 2.023
b.) 2.708
c.) 2.423
d.) 2.704
2. A study is conducted in patients with HIV. The primary outcome is CD4 cell count which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to use of supplements (coded as 1=yes, 0=no) and to duration of HIV, in years (i.e., the number of years between the diagnosis of HIV and the study date). For the analysis, Y=CD4 count.Y = 501.41 + 12.67 Supplements – 30.23 Duration of HIVA. What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years?Y = 438.505B. What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment?Y = 471.18C. What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years.= 425.835I would like to know if calculated correctly.…
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...
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- 2. A study is conducted in patients with HIV. The primary outcome is CD4 cell count which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to use of supplements(coded as l ves, 0-no) and to duration of HIV, in years(ie., the number of years between the diagnosis of HIV and the study date). For the analysis, Y-CD4 count. Y 501.41 12.67 Supplements - 30.23 Duration of HIV A. What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years? B. What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment? C. What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 yearsarrow_forwardA newspaper used an estimated regression equation to describe the relationship between y = error percentage for subjects reading a four-digit liquid crystal display and the independent variables x1 = level of backlight, x2 = character subtense, x3 = viewing angle, and x4 = level of ambient light. From a table given in the article, SSRegr = 21.6, SSResid = 22, and n = 30. What is the value of the test statistic F What is the P-value What is r2 What is Searrow_forwardZagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service. Predict the mean cost per person for a restaurant with a sum-mated rating of 50. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal? Location Food Décor Service Summated Rating Coded Location Cost Bins Midpoints City 22 14 19 55 0 33 19.99 25 City 20 15 20 55 0 26 29.99 35 City 23 19 21 63 0 43 39.99 45 City 19 18 18 55 0 32 49.99 55 City 24 16 18 58 0 44 59.99 65 City 22 22 21 65 0 44 69.99 75 City 22 20 20 62 0 50 79.99 85 City 20 19…arrow_forward
- A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age, X₂ = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 50 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Predictor Intercept AgeMed Bankrupt FedSpend HSGrad% Coefficient t-value = 4,198.5808 -27.3540 17.4893 -0.0124 -29.0314 SE 799.3395 12.5687 12.4033 0.0176 7.1268 tcalc p-value (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.)arrow_forwardA regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X1 = median age, X2 = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 45 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p- values to 4 decimal places.) Predictor Intercept AgeMed Coefficient SE tcalc p-value 4,641.0430 798.0634 -28.8630 12.4684 Bankrupt 20.1604 12.1079 FedSpend HSGrad% -0.0181 0.0181 -30.3196 7.1136 (b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.) -value =arrow_forwardAn article used an estimated regression equation to describe the relationship between y = error percentage for subjects reading a four-digit liquid crystal display and the independent variables x1 = level of backlight, x2 = character subtense, x3 = viewing angle, and x4 = level of ambient light. From a table given in the article, SSRegr = 20.4, SSResid = 21, and n = 30. Calculate the test statistic and calculate P- value. (Round your answer to two decimal places.) F = P- value=arrow_forward
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