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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

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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.2: Representing Data
Problem 22PFA
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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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