We are interested in whether there is a relationship between the ranking of a state and the area of the state.State# letters innameYear entered theUnionRank for entering theUnionArea (squaremiles)Alabama718192252,423Colorado8187638104,100Hawaii619595010,932Iowa418462956,276Maryland81788712,407Missouri818212469,709New Jersey9178738,722Ohio418031744,828SouthCarolina131788832,008Utah418964584,904Wisconsin918483065,499Part (a) Part (b) Part (c) Part (d)Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to two decimal places.)ŷ = + xPart (e)Find the correlation coefficient. (Round your answer to two decimal places.)What does it imply about the significance of the relationship?It implies there is a linear relationship between the variables.Part (f)Find the estimated areas for Utah and for Colorado. Are they close to the actual areas? (Round your answers to two decimal places.)Utah square milesColorado square milesPart (g) Part (h) Part (i) Part (j)Use the least squares line to estimate the area of a new state that enters the Union. (Round your answer to two decimal places.) square milesCan the least-squares line be used to predict it? Why or why not?Yes, the least-squares line produces a valid prediction and can be used.No, this is extrapolation and the least-squares line cannot be used. Part (k)Delete "Hawaii" and substitute "Alaska" for it. Alaska is the forty-ninth state with an area of 656,424 square miles.Calculate the new least-squares line. (Round your answers to two decimal places.)ŷ = + xPart (l)Find the estimated area for Utah. (Round your answer to two decimal places.) square milesIs it closer to the actual area with this new least-squares line or with the previous one that included Hawaii? Why do you think that's the case?The prediction with the least-squares line that includes is closest to the actual area of Utah. This is because seems to be an influential outlier.Part (m) Additional MaterialseBook

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We are interested in whether there is a relationship between the ranking of a state and the area of the state.

State	# letters in name	Year entered the Union	Rank for entering the Union	Area (square miles)
Alabama	7	1819	22	52,423
Colorado	8	1876	38	104,100
Hawaii	6	1959	50	10,932
Iowa	4	1846	29	56,276
Maryland	8	1788	7	12,407
Missouri	8	1821	24	69,709
New Jersey	9	1787	3	8,722
Ohio	4	1803	17	44,828
South Carolina	13	1788	8	32,008
Utah	4	1896	45	84,904
Wisconsin	9	1848	30	65,499

Part (a)
Part (b)
Part (c)
Part (d)

Calculate the least-squares line. Put the equation in the form of:
ŷ = a + bx.
(Round your answers to two decimal places.)

ŷ = + x
Part (e)

Find the correlation coefficient. (Round your answer to two decimal places.)

What does it imply about the significance of the relationship?
It implies there is a linear relationship between the variables.
Part (f)

Find the estimated areas for Utah and for Colorado. Are they close to the actual areas? (Round your answers to two decimal places.)

Utah square miles

Colorado square miles
Part (g)
Part (h)
Part (i)
Part (j)

Use the least squares line to estimate the area of a new state that enters the Union. (Round your answer to two decimal places.)
square miles

Can the least-squares line be used to predict it? Why or why not?

Yes, the least-squares line produces a valid prediction and can be used.No, this is extrapolation and the least-squares line cannot be used.
Part (k)

Delete "Hawaii" and substitute "Alaska" for it. Alaska is the forty-ninth state with an area of 656,424 square miles.

Calculate the new least-squares line. (Round your answers to two decimal places.)

ŷ = + x
Part (l)

Find the estimated area for Utah. (Round your answer to two decimal places.)
square miles

Is it closer to the actual area with this new least-squares line or with the previous one that included Hawaii? Why do you think that's the case?
The prediction with the least-squares line that includes is closest to the actual area of Utah. This is because seems to be an influential outlier.
Part (m)

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