Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Textbook Question
Chapter B.4, Problem 82E
Answer true or false to each of the following statements and explain your answers.
- a. Provided we do not extrapolate, multicollinearity does not affect the ability of a regression equation to predict the response variable.
- b. If x1 and x2 are predictor variables in a regression equation, the variable x3 =x1 + x2 can be added to the regression equation without affecting the VIF of x1 or x2.
- c. The severity of multicollinearity can be reduced by removing one or more highly intercorrelated predictor variables from the regression equation.
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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...
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- Olympic 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 following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forwardAnswer true or false to each of the following statements and explain your answers.a. In using the forward selection method, a predictor variable entered into the regression equation cannot be removed at a later step.b. In the backward elimination method, only one regression analysis needs to be obtained at each step.c. If a regression equation is determined by the forward selection method, the absolute value of the t-statistic for the utility of each predictor variable in the final regression equation must be greater than tenter.arrow_forward
- A)What would the consequence be for a regression model if the errors were not homoscedastic? (B) How might you proceed if you found that (b) were actually the case?arrow_forward.The worker has noticed that the more time he spends at work (x), the less money he is likely to make (y) in conducting transactions for his firm. Which of the regression equations MOST suggests such a possibility?arrow_forwardSuppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: ß1 = 0 and the alternative hypothesis Ha: ß1 ? 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?arrow_forward
- State whether each of the following statements is true or false. a. The error sum of squares must be smaller than the regression sum of squares. b. Instead of carrying out a multiple regression, we can get the same information from simple linear regressions of the dependent variable on each independent variable. c. The coefficient of determination cannot be negative. d. The adjusted coefficient of determination cannot be negative.e. The coefficient of multiple correlation is the square root of the coefficient of determination.arrow_forwardWhat can you say about SSE, SSR, and the utility of the regression equation for making predictions if a. r 2 = 1? b. r 2 = 0?arrow_forwardIf a new independent variable is added to a regression equation, the adjusted R2 increases only if the absolute value of the t-statistic of the new variable is greater than one. Group of answer choices True False.arrow_forward
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