Consider a regression model of workers' wages using vector-matrix notation andeducation data. Data are provided in the table below:Person123Education131510a) Using the information in the table above, discuss whether there is linearindependence in the above modelb) Compute the coefficient vector of this modelc) The researcher transformed the wage variable into natural log values using Stataand the education values were considered in terms of years. How could youinterpret the coefficient on education?d) Use the estimated coefficient vector to compute the total sum of squared errorε'ε.Wage1.822.141.56Constant111e) Compute the R² and explain how well education explains the variation in wages.f) Briefly comment on the reliability of the above result.

Given information: Person Wage Constant Education 1 1.82 1 13 2 2.14 1 15 3 1.56 1 10…

Answered: Consider a regression model of workers'…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section11.5: Choosing A Data Display

Problem 19E

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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?
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Reading is fundamental to a teenager's ability to perform well in school. Assume a researcher is interested in the ability of the number of books read over the summer to predict ACT Reading scores. Using a random sample of 10 random high school students the researchers recorded the number of books read over the summer and the students' ACT Reading scores. Books Read (X) ACT Score (Y) (X- Xmean) (Y - Ymean) (X-Xmean)(Y-Ymean) (X-Xmean)? (Y - Ymean)? 2 16 -5.4 -14.9 81 29 221 2 19 -5.4 -11.9 64 29 141 3 17 -4.4 -13.9 61 20 192 4 25 -3.4 -5.9 20 12 34 21 -3.4 -9.9 34 12 97 24 -1.4 -6.9 10 2 47 6 21 -1.4 -9.9 14 2 97 8 24 0.6 -6.9 -4 47 7 27 -0.4 -3.9 2 15 10 22 2.6 -8.9 -23 7 78 Total 52 216 259.1 113.3 969.3 МEAN 7.4 30.9 a. Identify the regression line using the number of books read to predict ACT Reading score. Use a = .05 to evaluate the quality of the prediction of the regression line. b. What is the predicted ACT Reading score when 5 books are read?
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A study was conducted to see if a person's income will affect their well-being. We want to create a model with Y = well-being index, and X = income in $1,000. The dependent variable in this study is: Income in $1,000 Well-being index Neither
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The data in the following table provide the relationship between breast-cancer incidence rate and menopausal status by age, based on Nurses’ Health Study (NHS) data from 1976-1990. The incidence rate for each group is given in two ways - first as cases/person-years and then as (cases per 100,000 person-years). Age Premenopausal Postmenopausal 35-39 124/131,704 (94) 15/14,795 (101) 40-44 264/179,132 (147) 47/43,583 (108) 45-49 304/151,548 (201) 163/90,965 (179) 50-54 159/61,215 (260) 401/184,597 (217) 55-59 25/6133 (408) 490/180,458 (272) Problem 1 Assess whether there is a difference between the incidence rate of breast cancer for premenopausal vs. postmenopausal women, controlling for age. Write out all 4 steps of the hypothesis test including a two-tailed -value. Problem 2 Provide a point estimate of the incidence rate ratio for postmenopausal vs. premenopausal women after controlling for age. Support your estimate with a 95%…
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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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