State # letters in name Year entered the Union Rank for entering the Union Area (square miles) Alabama 77 1819 2222 52,42352,423 Colorado 88 1876 3838 104,100104,100 Hawaii 66 1959 5050 10,93210,932 Iowa 44 1846 2929 56,27656,276 Maryland 88 1788 77 12,40712,407 Missouri 88 1821 2424 69,70969,709 New Jersey 99 1787 33 8,7228,722 Ohio 44 1803 1717 44,82844,828 South Carolina 1313 1788 88 32,00832,008 Utah 44 1896 4545 84,90484,904 Wisconsin 99 1848 3030 65,49965,499 We are interested in whether or not the number of letters in a state name depends upon the year the state entered the Union. (a) Decide which variable should be the independent variable and which should be the dependent variable. Year the state entered the Union is the Click for List variable and the number of letters in a state name is the Click for List variable (c) Does it appear from inspection that there is a relationship between the variables? Why or why not? There Click for List to be a relationship between the variables because the scatter plot Click for List a linear pattern. (d) Calculate the least-squares line. Use xx to represent the independent variable. Round any calculated values to two decimal places. y^=y^= (e) Find the correlation coefficient. Round your answer to two decimal places. The correlation coefficient is . (f) Find the estimated number of letters a state would have if it entered the Union in 1850 and 1940. Round your answers to the nearest integer. (i) The estimated number of letters a state would have if it entered the Union in 1850 is letters. (ii) The estimated number of letters a state would have if it entered the Union in 1940 is letters. (g) Does it appear that a line is the best way to fit the data? Why or why not? It Click for List appear that a line is the best way to fit the data because the correlation coefficient Click for List significant. (h) Use the least-squares line to estimate the number of letters a new state that enters the Union in 2005 would have. Can the least squares line be used to predict it? Why or why not? Round your answer to the nearest integer. The estimated number of letters a state would have if it entered the Union in 2005 is letters. The least squares line Click for List give an accurate estimate for that year because it is Click for List the range of observed xx values.
| State | # letters in name | Year entered the Union | Rank for entering the Union | Area (square miles) |
|---|---|---|---|---|
| Alabama | 77 | 1819 | 2222 | 52,42352,423 |
| Colorado | 88 | 1876 | 3838 | 104,100104,100 |
| Hawaii | 66 | 1959 | 5050 | 10,93210,932 |
| Iowa | 44 | 1846 | 2929 | 56,27656,276 |
| Maryland | 88 | 1788 | 77 | 12,40712,407 |
| Missouri | 88 | 1821 | 2424 | 69,70969,709 |
| New Jersey | 99 | 1787 | 33 | 8,7228,722 |
| Ohio | 44 | 1803 | 1717 | 44,82844,828 |
| South Carolina | 1313 | 1788 | 88 | 32,00832,008 |
| Utah | 44 | 1896 | 4545 | 84,90484,904 |
| Wisconsin | 99 | 1848 | 3030 | 65,49965,499 |
We are interested in whether or not the number of letters in a state name depends upon the year the state entered the Union.
(a) Decide which variable should be the independent variable and which should be the dependent variable.
Year the state entered the Union is the Click for List variable and the number of letters in a state name is the Click for List variable
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(c) Does it appear from inspection that there is a relationship between the variables? Why or why not?
There Click for List to be a relationship between the variables because the scatter plot Click for List a linear pattern.
(d) Calculate the least-squares line. Use xx to represent the independent variable.
Round any calculated values to two decimal places.
y^=y^=
(e) Find the correlation coefficient.
Round your answer to two decimal places.
The correlation coefficient is .
(f) Find the estimated number of letters a state would have if it entered the Union in 1850 and 1940.
Round your answers to the nearest integer.
(i) The estimated number of letters a state would have if it entered the Union in 1850 is letters.
(ii) The estimated number of letters a state would have if it entered the Union in 1940 is letters.
(g) Does it appear that a line is the best way to fit the data? Why or why not?
It Click for List appear that a line is the best way to fit the data because the correlation coefficient Click for List significant.
(h) Use the least-squares line to estimate the number of letters a new state that enters the Union in 2005 would have. Can the least squares line be used to predict it? Why or why not?
Round your answer to the nearest integer.
The estimated number of letters a state would have if it entered the Union in 2005 is letters.
The least squares line Click for List give an accurate estimate for that year because it is Click for List the range of observed xx values.
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