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 y=0.750x+48.28y = 0.750x + 48.28, which corresponds to option A.

Part 2: The coefficient of correlation rr is 0.9850.985, 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:

  1. How is the coefficient of correlation interpreted in this context?
  2. What does the slope of the regression line represent in terms of life expectancy?
  3. How could you calculate the life expectancy for other years using the regression equation?
  4. What does a strong correlation coefficient suggest about the reliability of the prediction for 2010?
  5. 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