shows the life expectancy for an individual born in the United States in certain years. Year of Birth Life Expectancy 1930 59.7 1940 62.9 1950 70.2 1965 69.7 1973 71.4 1982 74.5 1987 75 1992 75.7 2010 78.7 Table 12.20 Decide which variable should be the independent variable and which should be the dependent variable. Draw a scatter plot of the ordered pairs. Calculate the least squares line. Put the equation in the form of: ŷ = a + bx Find the correlation coefficient. Is it significant? Find the estimated life expectancy for an individual born in 1950 and for one born in 1982. Why aren’t the answers to part e the same as the values in Table 12.20 that correspond to those years? Use the two points in part e to plot the least squares line on your graph from part b. Based on the data, is there a linear relationship between the year of birth and life expectancy? Are there any outliers in the data? Using the least squares line, find the estimated life expectancy for an individual born in 1850. Does the least squares line give an accurate estimate for that year? Explain why or why not. What is the slope of the least-squares (best-fit) line? Interpret the slope.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
shows the life expectancy for an individual born in the United States in certain years.
|
Year of Birth Life Expectancy |
|
1930 59.7 |
|
1940 62.9 |
|
1950 70.2 |
|
1965 69.7 |
|
1973 71.4 |
|
1982 74.5 |
|
1987 75 |
|
1992 75.7 |
|
2010 78.7 |
Table 12.20
-
Decide which variable should be the independent variable and which should be the dependent variable.
-
Draw a scatter plot of the ordered pairs.
-
Calculate the least squares line. Put the equation in the form of: ŷ = a + bx
-
Find the
correlation coefficient . Is it significant? -
Find the estimated life expectancy for an individual born in 1950 and for one born in 1982.
-
Why aren’t the answers to part e the same as the values in Table 12.20 that correspond to those years?
-
Use the two points in part e to plot the least squares line on your graph from part b.
-
Based on the data, is there a linear relationship between the year of birth and life expectancy?
-
Are there any outliers in the data?
-
Using the least squares line, find the estimated life expectancy for an individual born in 1850. Does the least
squares line give an accurate estimate for that year? Explain why or why not.
-
What is the slope of the least-squares (best-fit) line? Interpret the slope.
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