Math Problem Statement
Fit a regression line to the data shown in the chart, and find the coefficient of correlation for the line. Use the regression line to predict life expectancy in the year 2010, where x is the number of decades after 1900. year, x 0 (1900) 2 (1920) 4 (1940) 6 (1960) 8 (1980) life expectancy, y 47.8 years 50.1 years 51.7 years 52.9 years 53.9 years Question content area bottom Part 1 Choose the correct regression line below. A.y equals 0.750 x plus 48.28 y equals 0.750 x plus 48.28 Your answer is correct.B.y equals 48.28 x plus 0.750 y equals 48.28 x plus 0.750 C.y equals 0.750 x minus 48.28 y equals 0.750 x minus 48.28 D.y equals 48.28 y equals 48.28 Part 2 The coefficient of correlation is enter your response here. (Round to three decimal places as needed.)
Solution
Part 1: The correct regression line is , which corresponds to option A.
Part 2: The coefficient of correlation is , indicating a very strong positive linear relationship.
Additionally, using the regression line to predict the life expectancy in the year 2010 (11 decades after 1900), we estimate it to be approximately 56.53 years.
Do you want more details or have any questions?
Here are 5 related questions:
- How is the coefficient of correlation interpreted in this context?
- What does the slope of the regression line represent in terms of life expectancy?
- How could you calculate the life expectancy for other years using the regression equation?
- What does a strong correlation coefficient suggest about the reliability of the prediction for 2010?
- Can we use this regression model for predicting life expectancy far beyond 2010?
Tip: Always verify if a linear relationship holds true by checking the correlation coefficient; values near 1 or -1 indicate strong linearity.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Correlation Coefficient
Prediction
Formulas
Linear regression equation: y = mx + b
Coefficient of correlation: r
Prediction formula using regression line
Theorems
Least Squares Method
Suitable Grade Level
Grades 10-12
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