**Statistical Analysis of Life Expectancy Over Time**In Talia's math class, students are encouraged to explore statistical questions with data. Curious about the increasing longevity in her family, Talia investigates if this trend is general by examining life expectancy data from the United States Center for Disease Control. The data collected since 1950 is as follows:| Years since 1950 | 0 | 10 | 20 | 30 | 40 | 45 | 50 | 55 | 60 | 64 ||------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|| Life Expectancy at Birth | 68.2 | 69.7 | 70.8 | 73.7 | 75.4 | 77.8 | 76.8 | 77.6 | 78.7 | 78.8 |### Analysis Processa) **Linear Regression Line**Using technology, the linear regression line is calculated and rounded to the nearest tenth:\[ y = 0.18x + 68.1 \]b) **Slope of the Regression Line**The slope of the regression line is \(0.737\).- **Meaning of the Slope**: Indicates the average increase in life expectancy at birth per year.c) **Y-intercept of the Regression Line**The y-intercept is \(68.1\).- **Meaning of the Y-intercept**: Represents the predicted life expectancy at birth in 1950.d) **Prediction for 2003**Talia, born in 2003, has a predicted life expectancy of \(77.6\) years.e) **Correlation Coefficient**The correlation coefficient is \(0.98\), indicating:- **Description of Correlation**: Strong positive correlation between the year of birth and life expectancy.This investigation highlights how statistical analysis can reveal trends in data over time, providing insights into societal changes such as increased longevity.

The given data is as follows: Years since 1950Life Expectancy at Birth068.21069.72070.83073.74075.44577.85076.85577.66078.76478.8a)XY068.2004651.241069.76971004858.092070.814164005012.643073.722119005431.694075.4301616005685.164577.8350120256052.845076.8384025005898.245577.6426830256021.766078.7472236006193.696478.85043.240966209.44Sum 374747.528714.21824656014.79Computing slopeComputing y-interceptThe regression line is .b)The slope is 0.2.Average increase in life expectancy at birth per year. Hence, the fifth option is correct.c)The y-intercept of the regression line is 68.1.Since, 1950 is the initial year, hence, it is predicted life expectancy at birth in 1950. Hence, the second option is correct.d)The predicted life expectancy at birth in 2003 is 70.7.e)The correlation coefficient is 0.98.There is a strong positive correlation.. Hence, the first option is correct.a) The regression line is .b) The slope is 0.2. The fifth option is correct which is "Average increase in life expectancy at birth per year".c) The y-intercept of the regression line is 68.1. The second option is correct which is "predicted life expectancy at birth in 1950".d) The predicted life expectancy at birth in 2003 is 70.7.e) The correlation coefficient is 0.98. The first option is correct which is "strong positive correlation".