Math Problem Statement

What is the answer

According to the regression line, the predicted maximum distance a road sign may be read for an individual that is 41 years old is about (round to the nearest tenths place).

Solution

To find the predicted maximum distance a road sign may be read for an individual who is 41 years old, we use the given least squares regression equation:

Distance=5773.01×Age\text{Distance} = 577 - 3.01 \times \text{Age}

Substitute Age=41\text{Age} = 41:

Distance=5773.01×41\text{Distance} = 577 - 3.01 \times 41

Now, calculate the value:

Distance=577123.41=453.59feet\text{Distance} = 577 - 123.41 = 453.59 \, \text{feet}

Rounding to the nearest tenth, the predicted distance is 453.6 feet.

So, the correct answer is 453.6 ft.


Would you like more details or have any other questions? Here are some related questions:

  1. What is the significance of the slope 3.01-3.01 in the regression equation?
  2. How is the correlation coefficient r=0.801r = -0.801 interpreted in this context?
  3. What does a negative correlation imply about age and distance in this scenario?
  4. How would the distance prediction change for a 30-year-old driver?
  5. What are some limitations of using linear regression for this type of prediction?

Tip: When interpreting the slope of a regression line, consider it as the average change in the dependent variable (distance) for each one-unit increase in the independent variable (age).

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Algebra

Formulas

Distance = 577 - 3.01 * Age

Theorems

Least Squares Regression

Suitable Grade Level

Grades 10-12