Concept explainers
(a)
To calculate: The regression line for number of natural science doctorates as a function of time t and
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(b)
The interpretation about the number of natural science doctorates by the help of slope of the regression line which is calculated in part (a). When the table representing the number of PhD graduates in Mexico every year is as follows:
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(c)
The variation in number of natural science doctorates with time from the graph which is calculated in part (a). When the table representing the number of PhD graduates in Mexico every year is as follows:
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(d)
Whether the conclusion is same as concluded in part (c) if r is equal to
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Applied Calculus
- Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forwardEnergy ConsumptionThe monthly residential consumption of energy in the U.S. for 2012 is found in the following table. Source: Energy Information Administration. Month Energytrillion BTU January 990.527 February 833.163 March 560.826 April 412.426 May 297.500 June 253.015 July 240.486 August 248.035 September 249.354 October 378.094 Number 631.203 December 838.265 Plot the data, letting t=1 correspond to January, t=2 to February, and so on. Is it reasonable to assume that the monthly consumption of energy is periodic? Find the trigonometric function of the form C(t)=asin(bt+c)+d that models these data when t is the month of the year and C(t) is the energy consumption. Graph the function on the same calculator window as the data. Estimate the total energy consumption for the year for residential customers in the United States and compare it to the actual value. Calculate the period of the function found in part b. Is this period reasonable?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forward
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