In this assignment, you will use the population data of Native Americans in the United States
from 1950 to 2020 to practice your skills in linear regression, interpolation, and extrapolation.
The following table shows the estimated Native American population in the US from 1950 to
2020: Year Native American Population 1950 332,000 1960 523,000 1970 800,000 1980
1,425,000 1990 1,878,285 2000 2,475,956 2010 2,932,248 2020 3,733,388 Note that these
estimates are based on the US Census Bureau's data and are subject to some margin of error.
Additionally, the definition of Native American used by the Census Bureau has changed over
time, which can affect the comparability of these numbers across different years. 1. Let x = 5
represent year 1950, x = 6 represent year 1960, and so on. Let y be the population in million
(rounded to the nearest tenth). Using the given data, calculate the equation of the leastsquares
line that represents the linear correlation between x and y. That yields y = 0.261x + 0.32 2.
Calculate the coefficient of correlation between x and y. That yields r = 0.93. What does this
value tell you about the strength and direction of the linear relationship between x and y? Explain
your answer in one or two sentences. 3. Explain in writing how to estimate the population of
Native Americans in the US in the year 2005 and tell your estimation. 4. Using your equation
from part 1, explain in writing how to estimate the population of Native Americans in the US in
the year 2025 and tell your estimation. 5. Explain the meaning of the coefficient of correlation in
the context of this problem. What is the range of possible values for the coefficient of
correlation? How does the coefficient of correlation relate to the strength and direction of the
linear relationship between x and y? 6. Verify the equation of the least squares line and the
coefficient of correlation using your own calculation. You can use any methods we discussed in
class. Are they correct?.
In this assignment, you will use the population data of Native Ameri.pdf
1. In this assignment, you will use the population data of Native Americans in the United States
from 1950 to 2020 to practice your skills in linear regression, interpolation, and extrapolation.
The following table shows the estimated Native American population in the US from 1950 to
2020: Year Native American Population 1950 332,000 1960 523,000 1970 800,000 1980
1,425,000 1990 1,878,285 2000 2,475,956 2010 2,932,248 2020 3,733,388 Note that these
estimates are based on the US Census Bureau's data and are subject to some margin of error.
Additionally, the definition of Native American used by the Census Bureau has changed over
time, which can affect the comparability of these numbers across different years. 1. Let x = 5
represent year 1950, x = 6 represent year 1960, and so on. Let y be the population in million
(rounded to the nearest tenth). Using the given data, calculate the equation of the leastsquares
line that represents the linear correlation between x and y. That yields y = 0.261x + 0.32 2.
Calculate the coefficient of correlation between x and y. That yields r = 0.93. What does this
value tell you about the strength and direction of the linear relationship between x and y? Explain
your answer in one or two sentences. 3. Explain in writing how to estimate the population of
Native Americans in the US in the year 2005 and tell your estimation. 4. Using your equation
from part 1, explain in writing how to estimate the population of Native Americans in the US in
the year 2025 and tell your estimation. 5. Explain the meaning of the coefficient of correlation in
the context of this problem. What is the range of possible values for the coefficient of
correlation? How does the coefficient of correlation relate to the strength and direction of the
linear relationship between x and y? 6. Verify the equation of the least squares line and the
coefficient of correlation using your own calculation. You can use any methods we discussed in
class. Are they correct?
