Use regression to find a quadratic model for the given data. (Round the terms to four decimal places.)0.60.72.64.75.3y-5.6 6.721.116.92.5y =Dlot the data along with the regression eauation

The regression equation (in the form of a quadratic equation) is given as: y=a+bx+cx2 ...(i)…

Answered: Use regression to find a quadratic…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.5: Quadratic Functions

Problem 17SBE

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A regression was run to determine whether there is arelationship between the diameter of a tree (x, in inches) and the tree’s age (y, in years). Theresults of the regression are given below. Use this topredict the age of a tree with diameter 10 inches. y=ax+ba=6.301b=1.044r=0.970
A Dubious Model of Oil Prices The following table shows the prices of oil in U.S. dollars per barrel, t years since 1990, One analysis involving additional data used a cubic equation to model this data. t Years since 1990 0 2 5 7 10 12 15 17 20 21 P Price, dollars per barrel 18.91 16.22 16.63 18.20 27.04 23.47 49.63 69.04 77.46 106.92 a. Use cubic regression to model these data. Round the regression parameters to four decimal places. b. Plot the data along with the cubic model. c. In the analysis mentioned above, the graph is expanded through 2020. Expand the viewing window to show the model from 1990 to 2020. d. What estimate does the model give for oil prices in 2015? e. The actual price of oil in December of 2015 was about 35 per barrel. What basic principle in the use of models would be violated in relying on the estimate in part d?
XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. 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 the stock price to be in January 2012? January 2013?
Life Expectancy The average life expectancy in the United States has been rising steadily over the past few decades, as shown in the table. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Use the linear model you found in part (b) to predict the life expectancy in the year 2006. (d) Search the Internet or your campus library to find the actual 2006 average life expectancy. Compare to your answer in part (c).
Remainder Round all answers to two decimal places unless otherwise indicated. Domestic Auto Sales in the United States For 2005 through 2008, the following table shows the total U.S. sales, in millions, of domestic automobiles excluding light trucks. Date Domestic cars sold 2005 5.53 2006 5.48 2007 5.25 2008 4.54 a.Get the equation of the regression line rounding parameters to two decimal places, and explain in practical terms the meaning of the slope. In particular, comment on the meaning of the sign of the slope. b.Plot the data points and the regression line. c.In 2009, 3.62 million domestic cars were sold in the United States. How does the forecast obtained from the regression line compare with this figure?
Alligators Refer to Exercise 93. If an alligator weighs 125 pounds, what is its approximate length? Round to the nearest inch. 93. Alligators The length in inches and weight in pounds of 25 alligators is shown in the table. Find the quadratic function that best fits the data. Round a,b, and c to six decimal places. Use the regression function to estimate the weight of an alligator that is 130 inches long. Round the weight to the nearest pound. Length Weight Length Weight Length Weight 94 130 72 38 90 106 74 51 128 366 89 84 147 640 85 84 68 39 58 28 82 80 76 42 86 80 86 83 114 197 94 110 88 70 90 102 63 33 72 61 78 57 86 90 74 54 69 36 61 44
TEST FOR UNDERSTANDING FOR EXAMPLE 5.16 In the study Economics of Scale in High School Operation by J. Riew, the author studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 enrollment. The data he observed were similar to those in the table below. n=enrollment 200 600 1000 1400 1800 C=costperstudent,indollars 667.4 545.0 461.0 415.4 408.2 Model these data using a quadratic function. Round regression parameters to four decimal places. According to this model, what enrollment produces the minimum cost per student?
Remainder Round all answers to two decimal places unless otherwise indicated. Gross Domestic Product U.S. gross domestic product, in trillions of dollars, is given in the table below. Date Gross domestic product 2010 15.0 2011 15.5 2012 16.2 2013 16.7 a.Find the equation of the regression line, and explain the meaning of its slope. Round regression line parameters to two decimal places. b.Plot the data points and the regression line. c.When would you predict that a gross domestic product of 17.3 trillion dollars would be reached? The actual gross domestic product in 2014 was 17.3 trillion dollars. What does that say about your prediction?

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Use regression to find a quadratic model for the given data. (Round the terms to four decimal places.) 0.6 0.7 2.6 4.7 5.3 -5.6 6.7 21.1 16.9 2.5