Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter B.3, Problem 63E
Consider the regression equation
y = β0 + β1 x1+ β2x2 +β3x3
with quantitative predictor variable x1 and indicator variables .x2 and x1, corresponding to one qualitative predictor variable. Interpret the hypothesis H0: β2 = 0 in terms of the regression lines associated with the three possible values of the qualitative predictor variable.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The equation used to predict college GPA (range 0-4.0) is y = 0.17 +0.51x, +0.002x,, where x, is high school GPA (range 0-4.0) and x, is college board score (range 200-800). Use the multiple regression equation to
predict college GPA for a high school GPA of 3.8 and a college board score of 500.
The predicted college GPA for a high school GPA of 3.8 and a college board score of 500 is
(Round to the nearest tenth as needed.)
The equation used to predict college GPA (range 0-4.0) is y=0.18+0.53x1+0.002x2, where x1 is high school GPA (range 0-4.0) and x2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.4 and a college board score of 500.
The predicted college GPA for a high school GPA of 3.4 and a college board score of 500 is ____.
(Round to the nearest tenth asneeded.)
Seventy-six Starbucks food items were analyzed for the calorie and carbohydrate content. We
used linear regression to explore the relationship between the number of calories and amount
of carbohydrates (in grams) Starbucks food menu items contain. The estimated regression
equation with carbohydrates as the response variable and the calories as the explanatory
variable is ŷ = 8.94 + 0.11x, and summary statistics of the two variables is provided below.
variable min
Q1 median
Q3
max
mean
sd
n missing
calories
80 300
350 420
500
338.8
105.4 77
carbohydrates
16
31
45
59
80
44.9
16.6 77
Chapter B Solutions
Introductory Statistics (10th Edition)
Ch. B.1 - Regarding the regression of a response variable,...Ch. B.1 - Fill in the blanks. a. The assumption that all...Ch. B.1 - Answer true or false to each of the following...Ch. B.1 - Prob. 4ECh. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - Prob. 6ECh. B.1 - Prob. 7ECh. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...
Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - Prob. 12ECh. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - Consider the scatterplot of y versus x in Output...Ch. B.1 - Consider the scatterplot of y versus x in Output...Ch. B.1 - Prob. 17ECh. B.1 - Prob. 18ECh. B.1 - If one or both of the assumptions of...Ch. B.1 - Prob. 20ECh. B.1 - Prob. 21ECh. B.1 - Prob. 22ECh. B.1 - Prob. 23ECh. B.1 - Gasoline Mileage Ratings. Gasoline mileage and...Ch. B.1 - Hip Fracture Rates. In the paper Very Low Rates of...Ch. B.1 - Prob. 26ECh. B.1 - Prob. 27ECh. B.1 - Prob. 28ECh. B.1 - Prob. 29ECh. B.1 - Gasoline Mileage Ratings. Refer to Exercise B.24,...Ch. B.1 - Hip Fracture Rates. Refer to Exercise B.25, where...Ch. B.1 - Drosophila Life-span. In the paper Extended...Ch. B.1 - Protein Content of Wheat. In their text, Methods...Ch. B.1 - Pine Tree Volume. Table B.2 on page B-5 provides...Ch. B.2 - Give an example of a. a second-degree polynomial...Ch. B.2 - In the polynomial regression equation y = 8 + 3x ...Ch. B.2 - Answer true or false to each of the following...Ch. B.2 - Explain why it is difficult to interpret the...Ch. B.2 - Fill in the blanks. a. A predictor variable is...Ch. B.2 - Answer true or false to each of the following...Ch. B.2 - Refer to the scatterplots in Outputs B.32(a) and...Ch. B.2 - Fill in the blanks. a. In the _______ method for...Ch. B.2 - Answer true or false to each of the following...Ch. B.2 - Stopping Distance. In their text Methods of...Ch. B.2 - Hour of Birth. In the paper increased Frequency of...Ch. B.2 - Silica Gel. Silica gel is a substance that absorbs...Ch. B.2 - Note: The data for the Using Technology exercises...Ch. B.2 - Hour of Birth. Refer to Exercise B.45, where the...Ch. B.2 - Silica Gel. Refer to Exercise B.46, where the...Ch. B.2 - Gasoline Mileage Ratings. Refer to Exercise B.24...Ch. B.2 - Protein Content of Wheat. Refer to Exercise B.33...Ch. B.2 - Satellite Orbits. Each issue of the magazine Ad...Ch. B.2 - Pine Tree Volume. In Example B.6 on page B-4, we...Ch. B.3 - Explain the difference between a quantitative...Ch. B.3 - In predicting a person's income, identify two...Ch. B.3 - In predicting the change in blood pressure for...Ch. B.3 - Fill in the blanks. a. A ___ predictor variable is...Ch. B.3 - Prob. 59ECh. B.3 - Answer true or false to each of the following...Ch. B.3 - For the regression equation y = 15 + 2x1 + 4x2 ...Ch. B.3 - Refer to Exercise B.61: a. Do the slopes of the...Ch. B.3 - Consider the regression equation y = 0 + 1 x1+ 2x2...Ch. B.3 - Prob. 64ECh. B.3 - Prob. 65ECh. B.3 - Prob. 66ECh. B.3 - Home Sale Prices. Refer to Example B.18 on page...Ch. B.3 - Mental Tasks and Drugs. In the text Statistical...Ch. B.3 - Gasoline Mileage Ratings. Refer to Exercise B.66...Ch. B.3 - Home Sale Prices. Refer to Exercise B.67 regarding...Ch. B.3 - Mental Tasks and Drugs. Refer to Exercise B.68...Ch. B.3 - Hip Fracture Rates. Refer to Exercise B.25 on page...Ch. B.3 - Television Viewing. The results of a study on...Ch. B.3 - Glue Strength. In the text Quality Control and...Ch. B.4 - Explain why the interpretation of the regression...Ch. B.4 - Answer true or false to each of the following...Ch. B.4 - Explain what is meant by multicollinearity.Ch. B.4 - Fill in the blanks. a. Consider a regression model...Ch. B.4 - Prob. 79ECh. B.4 - Prob. 80ECh. B.4 - Fill in the blanks. a. If predictor variable x1...Ch. B.4 - Answer true or false to each of the following...Ch. B.4 - State four ways to detect the presence of...Ch. B.4 - Prob. 84ECh. B.4 - Prob. 85ECh. B.4 - Prob. 86ECh. B.4 - Prob. 87ECh. B.4 - Prob. 88ECh. B.4 - Graduation Rates. Refer to Exercise B.86, where we...Ch. B.4 - Prob. 90ECh. B.4 - Gasoline Mileage Ratings. Refer to Exercise B.84,...Ch. B.4 - Graduation Rules. Refer to Exercise B.86, where we...Ch. B.5 - Explain what is meant by the variable selection...Ch. B.5 - Prob. 94ECh. B.5 - Fill in the blanks. a. In the forward selection...Ch. B.5 - Prob. 96ECh. B.5 - Answer true or false to each of the following...Ch. B.5 - Prob. 98ECh. B.5 - Prob. 99ECh. B.5 - Prob. 100ECh. B.5 - Prob. 101ECh. B.5 - Suppose that x1, x2, x3, and x4 are predictor...Ch. B.5 - Prob. 103ECh. B.5 - Graduation Rates. Refer to Exercise B.92 on page...Ch. B.5 - Home Sale Prices. In Example B. 18 on page B-67,...Ch. B.5 - Home Sale Prices. In Example B.18 on page B-67, we...Ch. B.5 - Infant Mortality Rates. In the article Children's...Ch. B.6 - Consider a multiple linear regression relating the...Ch. B.6 - Prob. 109ECh. B.6 - Prob. 110ECh. B.6 - Answer true or false to each of the following...Ch. B.6 - Explain the similarities and differences between...Ch. B.6 - Fill in the blanks. a. In the Mallows Cp...Ch. B.6 - Answer true or false to each of the following...Ch. B.6 - Gasoline Mileage Ratings. Refer to Exercise B.84...Ch. B.6 - Advertising and Sales. Refer to Exercise B.85 on...Ch. B.6 - Graduation Rates. Refer to Exercise B.86 on page...Ch. B.6 - Suppose that x1, x2, x3, and x4 are predictor...Ch. B.6 - Suppose that x1 x2, x3, and x4 are predictor...Ch. B.6 - Gasoline Mileage Ratings. Refer to Exercise B.91...Ch. B.6 - Graduation Rates. Refer to Exercise B.92 on page...Ch. B.6 - Home Sale Prices. Refer to Exercise B.105 on page...Ch. B.6 - Body Fat. Refer to Exercise B.106 on page B-143,...Ch. B.6 - Infant Mortality Rates. Refer to Exercise B.107 on...Ch. B.7 - List six problems that can arise in the collection...Ch. B.7 - Prob. 126ECh. B.7 - Prob. 127ECh. B.7 - Give an example of how a nonrepresentative sample...Ch. B.7 - Discuss the effect on a regression analysis of not...Ch. B.7 - Explain how multicollinearity can adversely affect...Ch. B.7 - Briefly describe what is meant by the problem of...Ch. B.7 - Answer true or false to each of the following...Ch. B.7 - Prob. 133ECh. B.7 - Discuss the advantages of using data collected...Ch. B.7 - Describe the potential effects of outliers on...Ch. B.7 - Prob. 136ECh. B.7 - Regarding regression analysis: a. What assumptions...Ch. B.7 - Answer true or false to each of the following...Ch. B.7 - Answer true or false to each of the following...Ch. B.7 - Discuss what G. E. P. Box might have meant when he...Ch. B.7 - Regarding model validation in regression: a. What...Ch. B - Explain what is meant when we say that a nonlinear...Ch. B - Answer true or false to the following statements...Ch. B - Prob. 3RPCh. B - Prob. 4RPCh. B - Answer true or false to each of the following...Ch. B - Paper Strength. In their text, Introduction to...Ch. B - Answer true or false to each of the following...Ch. B - Prob. 8RPCh. B - Explain what is meant when we say that a...Ch. B - OUTPUT B.95 Output for Problem 10 Regression...Ch. B - In regressing a response variable on several...Ch. B - Answer true or false to each of the following...Ch. B - Fill in the blanks. a. Multicollinearity is...Ch. B - Prob. 14RPCh. B - Explain why selecting a regression equation using...Ch. B - Answer true or false to each of the following...Ch. B - Fill in the blanks. a. In the _____ method, we...Ch. B - Patent Production. In the report The State New...Ch. B - Prob. 19RPCh. B - Prob. 20RPCh. B - Patent Production. Refer to Problem 18. where we...Ch. B - Prob. 22RPCh. B - Prob. 23RPCh. B - What are the possible consequences of the presence...Ch. B - Windmill Output. Refer to Problem 3, where we...Ch. B - Paper Strength. Refer to Problem 6, where we...Ch. B - Diabetes. Refer to Problem 10, where we considered...Ch. B - Hospital Stalling. Refer to Problem 14, where we...Ch. B - Patent Production. Refer to Problem 18, where we...Ch. B - Patent Production. Refer to Problem 29, where we...Ch. B - Recall from Chapter 1 of your text that the Focus...Ch. B - At the beginning of this module on page B-l, we...
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_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_forwardThe least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Interpret the slope.arrow_forward
- when a regression is used as a method of predicting dependent variables from one or more independent variables. How are the independent variables different from each other yet related to the dependent variable?arrow_forwardThe estimated regression equation for a model involving two independent variables and 10 observations follows.arrow_forwardWe have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.arrow_forward
- A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Using data collected for a sample ofn 91 houses in East Meadow, the appraiser fit the data with the following simple, linear regression model: y = 91.80 + 19.72, where x = number of rooms and y = appraised value of the house (in thousands of dollars). Additionally, the appraiser determined the coefficient of correlation to be r = .93 and the coefficient of determination to be r %3D = .86. Give a practical interpretation of the coefficient of correlation. B IUS Ix E三 三 三 E E E Insert Formula IIarrow_forwardFind the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables.arrow_forwardHormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. t HRT Use Breast Cancer Incidence 46.30 40.60 39.50 36.60 30.00 103.30 105.00 100.00 93.80 83.50 (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ŷ = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer incidence (in cases per 100,000 women) would be…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
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