A country's fertility rate can have a major long-term impact on its economic health. Low fertility rates eventually cause the average age of the population to skew higher, making it more difficult to fund programs such as social security. The following data represent a sample showing the number of children from 10 families: 1 5 3 1 2 2 1 4 0 1. a. Calculate the range. b. Calculate the variance. c. Calculate the standard deviation.
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Data for 26 Western Hemisphere countries can be used to examine the association between life expectancy and the birth rate (number of births per 1000 population). a) Create a scatterplot relating Life Expectancy to Birth Rate and describe the association. Are the regression assumptions satisfied? b) Is there an outlier? If so, set it aside and identify it before computing the regression. c) Find the equation of the regression line with the outlier removed. d) Make a plot of the residuals and comment. e) Is the line an appropriate model?. f) Interpret the value of $R^{2}$. $\mathrm{g}$ ) If government leaders want to increase life expectancy, should they encourage women to have fewer children? Explain.
For the fertility rate & life expectancy data, find the following: Blank #1: The correlation if it is an appropriate measure, to 4 decimal places. Otherwise, write the answer "not appropriate". Blank #2: The coefficient of determination, to 4 decimal places. Rewrite your value of the coefficient of determination for the fertility rate & life expectancy data as a percentage to two decimals and use it to interpret the meaning in context by filling in the appropriate blanks in the statement below. Do not include the % symbol in your first item answer. Approximately ______% of the variation in ______ is explained by its relationship with ______. Enter your answers to this as a list of items that fill in these blanks with no extra spaces and a comma separating each. For example, a valid answer might look like 15,variable,variable. Use the names of the variable as I have listed them in the problem. Blank # 1 Blank # 2 Blank # 3
Sri K.
Let kids denote the number of children ever born to a woman, and let $e d u c$ denote years of education for the woman. A simple model relating fertility to years of education is $$k i d s=\beta_{0}+\beta_{1} e d u c+u,$$ where $u$ is the unobserved error. i. What kinds of factors are contained in $u$ ? Are these likely to be correlated with level of education? ii. Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.
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