Final answer:
a. The slope and intercept of the regression line can be calculated to determine the rate of change and starting point of the line. b. The correlation coefficient of 0.986 indicates a strong positive linear relationship between years and median weekly earnings for both genders. c. The regression line equation can be used to predict the median weekly earnings for women in 2019. d. Limitations of correlation and regression include the lack of causation and assuming a linear relationship in real-world scenarios.
Step-by-step explanation:
a. Calculate the slope and intercept of the regression line for this data:
To calculate the slope and intercept of the regression line, we can use the formula: y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) represents the rate of change in median weekly earnings over time, and the y-intercept (b) represents the starting point of the regression line.
b. Interpret the meaning of the correlation coefficient in this context:
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this context, a correlation coefficient of 0.986 indicates a strong positive linear relationship between the years and the median weekly earnings for both men and women. This means that as the years increase, the median weekly earnings for both genders tend to increase as well.
c. Make a prediction for the median weekly earnings for women in the year 2019:
To make a prediction for the median weekly earnings for women in the year 2019, we can use the regression line equation. We substitute the year 2019 into the equation and solve for the predicted median weekly earnings for women.
d. Discuss the limitations of using correlation and regression in this scenario:
While correlation and regression analysis provide valuable insights into the relationship between variables, it's important to note their limitations. For example, correlation does not imply causation, meaning that a strong correlation between two variables does not necessarily mean one variable causes the other. Additionally, regression analysis assumes a linear relationship between the variables, which may not always be the case in real-world scenarios.