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 47.3 years 49.6 years 51.2 years 52.4 years 53.4 years Question content area bottom Part 1 Choose the correct regression line below. A.y equals 0.750 x minus 47.78 y equals 0.750 x minus 47.78 B.y equals 47.78 x plus 0.750 y equals 47.78 x plus 0.750 C.y equals 47.78 y equals 47.78 D.y equals 0.750 x plus 47.78 y equals 0.750 x plus 47.78 Your answer is correct. Part 2 The coefficient of correlation is    0.985. ​(Round to three decimal places as​ needed.) Part 3 The life expectancy in the year 2010 is    55. ​(Round to one decimal place as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Correlation
Prediction using a Regression Line

Formulas

Regression Line: y = mx + b
Correlation Coefficient (r)
Prediction Formula: Use regression line to predict y for a given x

Theorems

Least Squares Method for Regression
Pearson's Correlation Coefficient

Suitable Grade Level

Grades 10-12