Concept explainers
In Exercises 67-70, use technology to find the exponential regression function through the given points. (Round all coefficients to four decimal places.) [HINT: See Example 6.)
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Chapter 2 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
- World Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_forward5) Data are collected on starting salaries for graduating undergraduates and the GPA of the students and whether they were a business major (=1) or not (=0) a) Complete the table below b) What is the estimated regression equation? c) How much of the variation in income is explained by the regressors? d) What is the standard error of the error term in the regression equation?arrow_forward
- Review the table showing the balance in an investment account over time. Time (Years) Amount ($) 1 300 6 444 7 486 9 576 15 990 20 1,483 25 2,200 30 3,614 35 5,833 Which statement best describes the values of a and b in the regression model? In the power regression model, a represents the initial value and b represents the growth factor. In the power regression model, a represents the growth factor and b represents the initial value. In the exponential regression model, a represents the initial value and b represents the growth factor. In the exponential regression model, a represents the growth factor and b represents the initial value.arrow_forwardIllustrate Probit and Logit Regression?arrow_forward#23 Use the below data to create an equation of best fit. Is the linear equation better or worse than the exponential equation for modeling the trend of this data? How do you know? Use mathematical evidence to support your conclusion. x y 56 1.0 87 1.4 98 1.6 110 1.8 125 2.1 256 7.7 300 11.9arrow_forward
- 4. The table below shows the salary, in millions, made by the highest paid major league baseball player during certain years.year 1985 1991 1993 1996 1998 2001 salary 2.1 3.8 6.2 9.3 14.9 22 a) Find the regression equation.b) Predict the salary of the highest paid player in 2020.arrow_forwardDetermine whether the statements are true or false. A. In logistic regression, the model is fitted by using The Least Square Regression Estimation method. B. Odds ratio is defined as the ratio of two log-odds. C. In logistic regression, as Bo + Bx gets huge, p approaches 1.arrow_forwardThe regression equation to predict the total world gross ticket sales from the opening weekend ticket sales is: WorldGross^=9.23+6.87⋅OpeningWeekend Does a simple linear regression model seem appropriate for this data? Explain your answer in one or two sentences.arrow_forward
- What concepts can you learn in simple linear regression? Cite at least three techniques in solving regression analysis problemsarrow_forwardIllustrate the regression equation?arrow_forward3. Life ExpectancyWe have considered a regression equation to predict life expectancy from percent of government expenditure on health care, using data for a sample of 50 countries in SampCountries. Using technology and this dataset, find a 95% prediction interval for each of the following situations. (a) A country which puts only 3% of its expenditure into health care. Round your answers to one decimal place. (b) A country which puts 10% of its expenditure into health care. Round your answers to two decimal places. (c) A country which puts 50% of its expenditure into health care. Round your answers to two decimal places. Country Health LifeExpectancy Iceland 15.76 83.1 Kazakhstan 10.90 70.5 Lesotho 14.48 49.3 Uzbekistan 9.68 68.2 Peru 14.75 74.8 Iraq 5.99 69.5 Nicaragua 20.89 74.8 Zambia 12.57 58.1 Guinea-Bissau 7.79 54.3 Romania 12.17 74.5 United States 20.71 78.8 Sierra Leone 11.41 45.6 Malta 13.29 80.7 Luxembourg 13.64 81.8 Micronesia, Fed. Sts.…arrow_forward
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