3. 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 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: ? = a + bx d. Find the correlation coefficient. Is it significant? e. Find the estimated life expectancy for an individual born in 1950 and for one born in 1982. f. Why aren't the answers to part e the same as the values in the table 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.
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The independent variable should be the Year of Birth and the dependent variable should be the Life Expectancy. This is because the life expectancy depends on the year of birth. 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
Prediction
The bar graph gives the life expectancy for American men and women born in six selected years. you will use the data to obtain models for life expectancy and make predictions about how long American men and women will live in the future. Use the data for females shown in the bar graph at the bottom of the previous column to solve this exercise. a. Let $x$ represent the number of birth years after 1960 and let $y$ represent female life expectancy. Create a scatter plot that displays the data as a set of six points in a rectangular coordinate system. b. Draw a line through the two points that show female life expectancies for 1970 and $2000 .$ Use the coordinates of these points to write a linear function that models life expectancy, $E(x),$ for American women born $x$ years after $1960 .$ Round the slope to two decimal places. c. Use the function from part (b) to project the life expectancy of American women born in 2020 .
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