The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep: sleep = Bo + Bitotwrk + Bzeduc + Bzage + u, where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (See also Computer Exercise C3 in Chapter 2.) (i) If adults trade off sleep for work, what is the sign of B,? (ii) What signs do you think B2 and Bz will have? (iii) Using the data in SLEEP75, the estimated equation is sleep = 3,638.25 – .148 totwrk – 11.13 educ + 2.20 age n = 706, R? = .113. If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ. (v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk?

The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep: sleep = Bo + Bitotwrk + Bzeduc + Bzage + u, where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (See also Computer Exercise C3 in Chapter 2.) (i) If adults trade off sleep for work, what is the sign of B,? (ii) What signs do you think B2 and Bz will have? (iii) Using the data in SLEEP75, the estimated equation is sleep = 3,638.25 – .148 totwrk – 11.13 educ + 2.20 age n = 706, R? = .113. If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ. (v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
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.
Suppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARY�=�0+�1EXPERIENCE�+�2SERVICE�+�3INDUSTRIAL�+��. Is there enough evidence to support the claim that on average, CEOs in the service sector have lower salaries than CEOs in the financial sector at the 0.010.01 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Service (1 if service sector, 0 otherwise) Industrial (1 if industrial sector, 0 otherwise) Financial (1 if financial sector, 0 otherwise) 144225144225 1010 11 00 00 187765187765 2020 00 00 11 142500142500 66 11 00 00 169650169650 2828 11 00 00 167250167250 3131 00…
Suppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARY�=�0+�1EXPERIENCE�+�2SERVICE�+�3INDUSTRIAL�+��. Is there enough evidence to support the claim that on average, CEOs in the industrial sector have lower salaries than CEOs in the financial sector at the 0.050.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Copy Data CEO Salaries Salary Experience Service (1 if service sector, 0 otherwise) Industrial (1 if industrial sector, 0 otherwise) Financial (1 if financial sector, 0 otherwise) 141150141150 1010 11 00 00 176000176000 3232 11 00 00 139938139938 99 00 11 00 203577203577 3030 00 00 11 148032148032 22 00…
Suppose the following data were collected from a sample of 5 car manufacturers relating monthly car sales to the number of dealerships and the quarter of the year. Use statistical software to find the following regression equation: SALESi= b0 + b1DEALERSHIPSi + b2 QUARTER1i+ b3QUARTER2i + b4QUARTER3i+ ei Is there enough evidence to support the claim that on average, car sales are higher in the 4th quarter than in the 2nd quarter at the 0.01 level of significance? If yes, write the regression equation in the spaces provided, rounded to two decimal places. Else, select "There is not enough evidence." Monthly Sales Number of Dealerships 1st Quarter (1 if Jan.-Mar., 0 otherwise) 2nd Quarter (1 if Apr.-Jun., 0 otherwise) 3rd Quarter (1 if Jul.-Sep., 0 otherwise) 4th Quarter (1 if Oct.-Dec., 0 otherwise) 85482 4 1 0 0 0 101319 9 1 0 0 0 121389 12 1 0 0 0 133677 18 1 0 0 0 194588 22 1 0 0 0 82128 4 0 1 0 0 150407 9 0 1 0 0 242714 12 0…
Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept)ageheightforearm Estimate10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedomMultiple R-squared: 0.01983, Adjusted R-squared: 0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 Which of the following is the correct interpretation of the Adjusted R-squared? The probability that our model…