The table below 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 1. Find the correlation coefficient r. (Round your answer to four decimal places.) 2. Find the estimated life expectancy for an individual born in 1973 and for one born in 1982. (Round your answers to one decimal place) a) Birthdate in 1973: _______ b) Birthdate in 1982: _______ 3) Why aren't the answers to part (e) the same as the values in the table that correspond to those years? a. The answers are different because of errors in recording the life expectancy. b. The answers will be different each time you calculate a least squares line. c. The answers are different because people live longer each year. d. The answers are different because not all data points will fall on the regression line unless the correlation is perfect.
Added by -Ngel B.
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To find the correlation coefficient r, we first need to calculate the mean of the years and the mean of the life expectancies. Then we calculate the differences between each year and the mean year, and each life expectancy and the mean life expectancy. We square Show more…
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Table 12.20 shows the life expectancy for an individual born in the United States in certain years. $$\begin{array}{|c|c|}\hline \text { Year of Birth } & {\text { Life Expectancy }} \\ \hline 1930 & {59.7} \\ \hline 1940 & {62.9} \\ \hline 1950 & {70.2} \\ \hline 1950 & {71.5} \\ \hline 1987 & {75} \\ \hline 1987 & {75.7} \\ \hline 2010 & {78.7} \\ \hline\end{array}$$ a. Decide which variable should be the independent variable and which should be the dependent variable. b. Draw a scatter plot of the ordered pairs. c. Calculate the least squares line. Put the equation in the form of: $\hat{y}=a+b x$ d. Find the correlation coefficient. Is it significant? e. Find the estimated life expectancy for an indidual born in 1950 and for one born in 1982 f. Why aren't the answers to part e the same as the values in Table 12.20 that correspond to those years? g. Use the two points in part e to plot the least squares line on your graph from part b. h. Based on the data, is there a linear relationship between the year of birth and life expectancy? i. Are there any outliers in the data? j. 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. k. What is the slope of the least-squares (best-fit) line? Interpret the slope.
Linear Regression and Correlation
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The following table shows the average life expectancy, in years, of a child born in the given year. Year Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 (a) Find the equation of the regression line. (Let E be the life expectancy in years and t the number of years since 2005. Round regression line parameters to two decimal places.) E(t) = 0.15t + 77.74 (b) Plot the data points and the regression line. (c) Explain in practical terms the meaning of the slope of the regression line. (Round your answer to two decimal places.) For each increase of 1 in the year of birth, the life expectancy increases by 0.15 years. (d) Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2018? (Round your answer to one decimal place.) 79.9 years (e) Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1550? (Round your answer to one decimal place.) 29.9 years What do you predict as the life expectancy of a child born in 2400? (Round your answer to one decimal place.) 117.4 years
Donna D.
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