Need help on the last three (The ones with x's) (D) and (E) The following table shows the average life expectancy, in years, of a childborn in the given year.tYearLife expectancy200577.6200778.1200978.5201178.7201378.8(a) Find the equation of the regression line. (Let E be the lifeexpectancy in years andt the number of years since 2005. Roundregression line parameters to two decimal places.)E(t) =.15t + 77.74(b) Plot the data points and the regression line.EE7979787877246824.68EE79797878777724682468(c) Explain in practical terms the meaning of the slope of the regressionline. (Round your answer to two decimal places.)For each increase of 1 in the year of birth the life expectancyincreases by 15v year.(d) Based on the trend of the regression line, what do you predict asthe life expectancy of a child born in 2019? (Round your answer to onedecimal place.)79.4 x yr(e) Based on the trend of the regression line, what do you predict as thelife expectancy of a child born in 1580? (Round your answer to onedecimal place.)34.5 x yrWhat do you predict as the life expectancy of a child born in 2300?(Round your answer to one decimal places.)107.5 x yr

Name: Need help on the last three (The ones with x's) (D) and (E) The follow
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Description: Need help on the last three (The ones with x's) (D) and (E) The following table shows the average life expectancy, in years, of a childborn in the given year.tYearLife expectancy200577.6200778.1200978.5201178.7201378.8(a) Find the equation of the reg

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Need help on the last three (The ones with x's) (D) and (E)

The following table shows the average life expectancy, in years, of a child
born in the given year.t
Year
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. (Let E be the life
expectancy in years andt the number of years since 2005. Round
regression line parameters to two decimal places.)
E(t) =.15t + 77.74
(b) Plot the data points and the regression line.
E
E
79
79
78
78
77
2
4
6
8
2
4.
6
8
E
E
79
79
78
78
77
77
2
4
6
8
2
4
6
8
(c) Explain in practical terms the meaning of the slope of the regression
line. (Round your answer to two decimal places.)
For each increase of 1 in the year of birth the life expectancy
increases by 15
v year.
(d) Based on the trend of the regression line, what do you predict as
the life expectancy of a child born in 2019? (Round your answer to one
decimal place.)
79.4 x yr
(e) Based on the trend of the regression line, what do you predict as the
life expectancy of a child born in 1580? (Round your answer to one
decimal place.)
34.5 x yr
What do you predict as the life expectancy of a child born in 2300?
(Round your answer to one decimal places.)
107.5 x yr

Expert Solution

Step 1

For part d:

The objective is to predict the life expectancy of a child born in 2019.

Step 2

According to the part a the equation for linear regression line is given by the formula:

E(t)=.15t+77.74; where year 2005 is taken as the initial year, i.e. t=0 when year is 2005.

Now to predict the life expectancy of a child born in 2019 first find the t since 2005, as

t=2019-2005=14

Now the life expectancy of a child born in 2019 can be calculated by finding E(t) when t=14, as

$\begin{matrix} E (14) = .15 (14) + 77.74 \\ = 2.1 + 77.74 = 79.84 \end{matrix}$

Thus, life expectancy of a child born in 2019 is approx. 79.8 years.

Step 3

For part e:

The objective is to predict the life expectancy of a child born in 1580.

Step by step

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