S of 14The relationship between x = height of a student (in inches) and y = number of steps required to walk the length of a schoolhallway, is summarized with the regression line ŷ = 113.6 - 0.921x. For this model, technology gives s = 3.50 and = 0.399 .Interpret the value of s.O The actual number of strides required to walk the length of a school hallway is typically about 3.50 less than the numberpredicted by the least-squares regression line with x= height of a student (in inches).O The number predicted by the least-squares regression line is typically about 3.50 away from the actual number of stridesrequired to walk the length of a school hallway with x height of a student (in inches).O The actual number of strides required to walk the length of a school hallway is typically about 3.50 units away from thenumber predicted by the least-squares regression line with x height of a student (in inches).O The actual number of strides required to walk the length of a school hallway is always about 3.50 away from the numberpredicted by the least-squares regression line with x = height of a student (in inches).O The actual number of strides required to walk the length of a school hallway is typically about 3.50 more than thenumber predicted by the least-squares regression line with x = height of a student (in inches).

here given for the regression output between two variable x= height of student y=no of steps…

The relationship between x = height of a student (in inches) and y = number of steps required to walk the length of a school hallway, is summarized with the regression line ŷ = 113.6 – 0.921x. For this model, technology gives s 3.50 and= 0.399. %3D y%3D %3D %3D Interpret the value of s. O The actual pumber of strides reguired to walk the length of a school hallway is tynically about 3 50 less than the number

The relationship between x = height of a student (in inches) and y = number of steps required to walk the length of a school hallway, is summarized with the regression line ŷ = 113.6 – 0.921x. For this model, technology gives s 3.50 and= 0.399. %3D y%3D %3D %3D Interpret the value of s. O The actual pumber of strides reguired to walk the length of a school hallway is tynically about 3 50 less than the number

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

Chapter4: Exponential Functions

Section4.4: Modeling Nearly Exponential Data

Problem 4E: Special Rounding Instructions For this exercise set, round all regression parameters to three...

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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?
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?
For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Growth in Length of HaddockA study by Raitt showed that the maximum length that a haddock could be expected to grow is about 53centimeters.Let D=D(t) denote the difference between 53centimeters and the length at age t years. The table below gives experimentally collected values for D. Age t Difference D 2 28.2 5 16.1 7 9.5 13 3.3 19 1.0 a.Find an exponential model of D as a function of t. b.Let L=L(t) denote the length in centimeters of a haddock at age t years. Find the model for L as a function of t. c.Plot the graph of the experimentally gathered data for the length L at ages 2,5,7,13, and 19years along with the graph of the model you made for L. Does this graph show that the 5year old haddock is a bit shorter or a bit longer than would be expected? d.A fisherman has caught a haddock that measures 41centimeters. What is the approximate age of the haddock?
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?
For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.
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
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Atmospheric Pressure The table below gives a measurement of atmospheric pressure, in grams per square centimeter, at the given altitude, in kilometers. Altitude Atmospheric Pressure 5 569 10 313 15 172 20 95 25 52 For comparison, 1 kilometer is about 0.6 mile, and 1 gram per square centimeter is about 2 pounds per square foot. a.Plot the data on atmospheric pressure. b.Make an exponential model for the data on atmospheric pressure. c.What is the atmospheric pressure at an altitude of 30 kilometers? d.Find the atmospheric pressure on Earths surface. This is termed standard atmospheric pressure. e.At what altitude is the atmospheric pressure equal to 25 of standard atmospheric pressure?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.
For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy