The table shows how the percent of women in the civilian...

The table shows how the percent of women in the civilian workforce has changed from 1970 to 2010 $$\begin{array}{l|c} \text { Year } & \begin{array}{c} \text { Percent of Women in } \\ \text { the Workforce } \end{array} \\ \hline 1970 & 43.3 \\ 1975 & 46.3 \\ 1980 & 51.5 \\ 1985 & 54.5 \\ 1990 & 57.5 \\ 1995 & 58.9 \\ 2000 & 59.9 \\ 2005 & 59.0 \\ 2010 & 58.6 \end{array}$$ (a) Use a calculator to find the least-squares regression line for these data, where $x$ is the number of years after 1970 (b) Based on your result from part (a), write an equation that yields the same $y$ -values when the actual year is entered. (c) Predict the percent of population of women in the civilian workforce in 2015 .

The table shows how the percent of women in the civilian workforce has changed from 1970 to 2010
$$\begin{array}{l|c} \text { Year } & \begin{array}{c} \text { Percent of Women in } \\ \text { the Workforce } \end{array} \\ \hline 1970 & 43.3 \\ 1975 & 46.3 \\ 1980 & 51.5 \\ 1985 & 54.5 \\ 1990 & 57.5 \\ 1995 & 58.9 \\ 2000 & 59.9 \\ 2005 & 59.0 \\ 2010 & 58.6 \end{array}$$
(a) Use a calculator to find the least-squares regression line for these data, where $x$ is the number of years after 1970
(b) Based on your result from part (a), write an equation that yields the same $y$ -values when the actual year is entered.
(c) Predict the percent of population of women in the civilian workforce in 2015 .

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Key Concepts

Transformation of Variables

In many problems, the independent variable is transformed to simplify the computation or interpretation of a regression model. For example, setting x as the number of years after a base year converts the original time data into a format that is easier to handle mathematically, and this transformation can later be reversed to express the model in terms of the actual variable (year in this case).

Extrapolation and Prediction

Once a regression model is established, it can be used to predict values outside the observed data range by substituting new values for the independent variable. Extrapolation involves using the model to estimate outcomes for dates or conditions beyond those in the dataset, although this should be done cautiously since the relationship may not hold outside the original range of data.

Least-Squares Regression

This is a statistical method used to determine the straight line that best fits a set of data points by minimizing the sum of the squares of the vertical distances (residuals) of the points from the line. It provides a predictive model where one can understand and estimate the relationship between an independent variable (such as time) and a dependent variable (such as percent participation) in the dataset.

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