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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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
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 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…
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We 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.
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Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 Why is the interpretation of the constant term (i.e. "intercept") not meaningful for this example? The predicted area will be negative when the number of cabinets is zero and the height of the kitchen is also zero. But we cannot have a negative area, nor a kitchen ceiling height of 0 inches.…
Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 What is the predicted area of a kitchen with a height of 96 inches and 10 cabinets? Report your answer to 1 decimal place. square feet
The rental of an apartment (R) near campus is a function of the square footage (Sq). A random sample of apartments near campus yielded the following summary statistics: R= $350, Sq = 100, sR = $ 30, and 8 są = 10. Suppose also that the correlation between price and weight is 0.8. (a) Write the implied least squares linear regression equation. (b) Suppose an apartment has 75 sqft. Predict its price based on the above model. (c) Suppose the true rental of the apartment in part (b) is $ 325. What is the value of the residual?