Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Textbook Question
Chapter 14.3, Problem 117E
As we noted, because of the regression identity, we can express the coefficient of determination in terms of the total sum of squares and the error sum of squares as r2 = 1 - SSE/SST.
- a. Explain why this formula shows that the coefficient of determination can also be interpreted as the percentage reduction obtained in the total squared error by using the regression equation instead of the
mean , ȳ, to predict the observed values of the response variable. - b. Refer to Exercise 14.99. What percentage reduction is obtained in the total squared error by using the regression equation instead of the mean of the observed prices to predict the observed prices?
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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.
A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows:
SP = -20; SSx = 4; My = 7; Mx = 3
What is b equal to?
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Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
To test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.
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Chapter 14 Solutions
Introductory Statistics (10th Edition)
Ch. 14.1 - Regarding linear equations with one independent...Ch. 14.1 - Prob. 2ECh. 14.1 - Consider the linear equation y = b0 + b1x. a....Ch. 14.1 - Prob. 4ECh. 14.1 - In Exercises 14.514.14, we give linear equations....Ch. 14.1 - Prob. 6ECh. 14.1 - In Exercises 14.5-14.14, we give linear equations....Ch. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - In Exercises 14.514.14, we give linear equations....
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - In Exercises 14.1514.22,we identify the...Ch. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Rental-Car Costs. During one month, the Avis...Ch. 14.1 - Air-Conditioning Repairs. Richards Healing and...Ch. 14.1 - Measuring Temperature. The two most commonly used...Ch. 14.1 - A Law of Physics. A ball is thrown straight up in...Ch. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Prob. 31ECh. 14.1 - Road Grade. The grade of a road is defined as the...Ch. 14.1 - Vertical Lines. In this section, we stated that...Ch. 14.2 - Regarding a scatterplot, a. identify one of its...Ch. 14.2 - Regarding the criterion used to decide on the line...Ch. 14.2 - Regarding the line that best fits a set of data...Ch. 14.2 - Regarding the two variables under consideration in...Ch. 14.2 - Using the regression equation to make predictions...Ch. 14.2 - Fill in the blanks. a. In the context of...Ch. 14.2 - For which of the following sets of data points can...Ch. 14.2 - For which of the following sets of data points can...Ch. 14.2 - In each of Exercises 14.4214.45, we have presented...Ch. 14.2 - In each of Exercises 14.4214.45, we have presented...Ch. 14.2 - In each of Exercises 14.4214.45, we have presented...Ch. 14.2 - In each of Exercises 14.4214.45, we have presented...Ch. 14.2 - For a data set consisting of two data points: a....Ch. 14.2 - Prob. 47ECh. 14.2 - In each of Exercises 14.4814.57, a. find the...Ch. 14.2 - In each of Exercises 14.4814.57. a. find the...Ch. 14.2 - In each of Exercises 14.4814.57, a. find the...Ch. 14.2 - In each of Exercises 14.48-14.57, a. find the...Ch. 14.2 - In each of Exercises 14.4814.57, a. find the...Ch. 14.2 - In each of Exercises 14.4814.57, a. find the...Ch. 14.2 - In each of Exercises 14.48-14.57, a. find the...Ch. 14.2 - In each of Exercises 14.4814.57. a. find the...Ch. 14.2 - In each of Exercises 14.4814.57. a. find the...Ch. 14.2 - In each of Exercises 14.4814.57. a. find the...Ch. 14.2 - Prob. 58ECh. 14.2 - In each of Exercises 14.5814.63, a. find the...Ch. 14.2 - In each of Exercises 14.5814.63. a. find the...Ch. 14.2 - In each of Exercises 14.5814.63, a. find the...Ch. 14.2 - In each of Exercises 14.5814.63. a. find the...Ch. 14.2 - In each of Exercises 14.5814.63, a. find the...Ch. 14.2 - Tax Efficiency. In Exercise 14.58, you determined...Ch. 14.2 - Corvette Prices. In Exercise 14.59, you determined...Ch. 14.2 - Anscombes Quartet. In the article Graphs in...Ch. 14.2 - Study Time and Score. The negative relation...Ch. 14.2 - Age and Price of Orions. In Table 14.2, we...Ch. 14.2 - Wasp Mating Systems. In the paper "Mating System...Ch. 14.2 - In Exercises 14.7014.80, use the technology of...Ch. 14.2 - In Exercises 14.7014.80, use the technology of...Ch. 14.2 - In Exercises 14.7014.80, use the technology of...Ch. 14.2 - In Exercises I4.7014.80, use the technology of...Ch. 14.2 - In Exercises 14.7014.80, use the technology of...Ch. 14.2 - In Exercises 14.7014.80, use the technology of...Ch. 14.2 - Prob. 76ECh. 14.2 - Prob. 77ECh. 14.2 - Prob. 78ECh. 14.2 - Prob. 79ECh. 14.2 - In Exercises 14.7014.80, use the technology of...Ch. 14.2 - Prob. 81ECh. 14.2 - Time Series. A collection of observations of a...Ch. 14.3 - In this section, we introduced a descriptive...Ch. 14.3 - A measure of total variation in the observed...Ch. 14.3 - A measure of the amount of variation in the...Ch. 14.3 - A measure of the amount of variation in the...Ch. 14.3 - Prob. 87ECh. 14.3 - In Exercises 14.8814.97, we repeal the data and...Ch. 14.3 - In Exercises14.481497, we repeal the tiara and...Ch. 14.3 - In Exercises 14.8814.97, we repeat the data and...Ch. 14.3 - Prob. 91ECh. 14.3 - Prob. 92ECh. 14.3 - Prob. 93ECh. 14.3 - Prob. 94ECh. 14.3 - Prob. 95ECh. 14.3 - Prob. 96ECh. 14.3 - Prob. 97ECh. 14.3 - Applying the Concepts and Skills For Exercises...Ch. 14.3 - Prob. 99ECh. 14.3 - Prob. 100ECh. 14.3 - Prob. 101ECh. 14.3 - Prob. 102ECh. 14.3 - For Exercises 14.9814.103, a. compute SST, SSR,...Ch. 14.3 - Prob. 104ECh. 14.3 - In Exercises 14.10414.115, use the technology of...Ch. 14.3 - Prob. 106ECh. 14.3 - Prob. 107ECh. 14.3 - Prob. 108ECh. 14.3 - Prob. 109ECh. 14.3 - Prob. 110ECh. 14.3 - Prob. 111ECh. 14.3 - Prob. 112ECh. 14.3 - Prob. 113ECh. 14.3 - In Exercises 14.10414.115, use the technology of...Ch. 14.3 - In Exercises 14.10414.115, use the technology of...Ch. 14.3 - What can you say about SSE, SSR, and the utility...Ch. 14.3 - As we noted, because of the regression identity,...Ch. 14.4 - What is one purpose of the linear correlation...Ch. 14.4 - Prob. 119ECh. 14.4 - The symbol that is used for the linear correlation...Ch. 14.4 - A value of r close to 1 indicates that there is a...Ch. 14.4 - A value of r close to ____ indicates that there is...Ch. 14.4 - A value of r close to ____ indicates that the...Ch. 14.4 - A value of r close to 0 indicates that the...Ch. 14.4 - If y tends to increase linearly as x increases,...Ch. 14.4 - If y lends to decrease linearly as x increases,...Ch. 14.4 - If there is no linear relationship between x and...Ch. 14.4 - In each of Exercises 14.12814.130, determine...Ch. 14.4 - In each of Exercises 14.12814.130, determine...Ch. 14.4 - In each of Exercises 14.12814.130, determine...Ch. 14.4 - Answer true or false to the following statement...Ch. 14.4 - The linear correlation coefficient of a set of...Ch. 14.4 - The coefficient of determination of a set of data...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data front...Ch. 14.4 - Prob. 137ECh. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.13414.143, we repeat data from...Ch. 14.4 - In Exercises 14.14414.149, we repeat data from...Ch. 14.4 - In Exercises 14.14414.149, we repeat data from...Ch. 14.4 - In Exercises 14.14414.149, we repeat data from...Ch. 14.4 - Prob. 147ECh. 14.4 - In Exercises 14.14414.149, we repeat data from...Ch. 14.4 - In Exercises 14.14414.149, we repeat data from...Ch. 14.4 - Height and Score. A random sample of 10 students...Ch. 14.4 - Prob. 151ECh. 14.4 - Prob. 152ECh. 14.4 - Prob. 153ECh. 14.4 - Prob. 154ECh. 14.4 - In Exercise 14.154-14.166, use the technology of...Ch. 14.4 - Prob. 156ECh. 14.4 - Prob. 157ECh. 14.4 - Prob. 158ECh. 14.4 - Prob. 159ECh. 14.4 - Prob. 160ECh. 14.4 - Prob. 161ECh. 14.4 - In Exercises 14.154-14.166, use the technology of...Ch. 14.4 - In Exercises 14.15414.166, use the technology of...Ch. 14.4 - Prob. 164ECh. 14.4 - Prob. 165ECh. 14.4 - In Exercises 14.154-14.166, use the technology of...Ch. 14.4 - The coefficient of determination of a set of data...Ch. 14.4 - Country Music Blues. A Knight-Ridder News Service...Ch. 14.4 - Prob. 169ECh. 14.4 - In each of Exercises 14.169 and 14.170, a....Ch. 14 - For a linear equation y = b0 + b1x, identify the ...Ch. 14 - Consider the linear equation y = 4-3x. a. At what...Ch. 14 - In Problems 35, answer true or false to each...Ch. 14 - In Problems 35, answer true or false to each...Ch. 14 - In Problems 35, answer true or false to each...Ch. 14 - Prob. 6RPCh. 14 - In Problems 35, answer true or false to each...Ch. 14 - Prob. 8RPCh. 14 - In each of Problems 911, fill in the blank. 9....Ch. 14 - Prob. 10RPCh. 14 - Prob. 11RPCh. 14 - Prob. 12RPCh. 14 - Prob. 13RPCh. 14 - Prob. 14RPCh. 14 - Prob. 15RPCh. 14 - Prob. 16RPCh. 14 - Prob. 17RPCh. 14 - Prob. 18RPCh. 14 - Prob. 19RPCh. 14 - Equipment Depreciation. A small company has...Ch. 14 - Graduation Rates. Graduation ratethe percentage of...Ch. 14 - Graduation Rates. Refer to Problem 21. a....Ch. 14 - Graduation Rates. Refer to Problem 21. a. Compute...Ch. 14 - Exotic Plants. In the article Effects of Human...Ch. 14 - In Problems 2527, use the technology of your...Ch. 14 - Prob. 26RPCh. 14 - Prob. 27RPCh. 14 - Recall from Chapter 1 (see page 34) that the Focus...Ch. 14 - At the beginning of this chapter, we presented...
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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
- The 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_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_forwardConsider the following four quantities for a regression coefficient: the estimate of the coefficient, the standard error of the coefficient, the t-value of the coefficient, and the p-value of the coefficient. Which of the following is true? a. If the standard error increases and the estimate itself doesn't change, the magnitude of the t-value will decrease and the p-value will decrease. b. If the standard error decreases and the estimate itself doesn't change, the magnitude of the t-value will increase and the p-value will decrease. c. If the standard error decreases and the estimate itself doesn't change, the magnitude of the t-value will increase and the p-value will increase. d. If the standard error increases and the estimate itself doesn't change, the magnitude of the t-value will increase and the p-value will decrease.arrow_forward
- The overall purpose of regression analysis is: a) to lessen our error in making predictions b) to make perfect predictions, since all data points must fall on the regression line c) to exploit the correlation between Y and X and use it to help make better predictions of Y d) two of the above e) three of the above f) none of the abovearrow_forwardA sample of X and Y scores is taken, and a regression line is used to predict Y from X. If SSY' = 300, SSE = 500, and N = 50, what is(a) SSY?(b) the standard error of the estimate?(c) R2?arrow_forwardSuppose that R2 = 0 for a data set. What can you say abouta. SSE?b. SSR?c. the utility of the sample multiple linear regression equation for making predictions?arrow_forward
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