Question

what is the slope of the linear regression prediction equation if a person with 12 years of schooling earns $31,000 per year and a person with 13 years of schooling earns $32,500 per year?
answer

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x \) represents years of schooling and \( y \) represents earnings. Let \((x_1, y_1)=(12, 31000)\) and \((x_2, y_2)=(13, 32500)\).

Step2: Substitute values into formula

Substitute \( x_1 = 12 \), \( y_1 = 31000 \), \( x_2 = 13 \), \( y_2 = 32500 \) into the slope formula: \( m=\frac{32500 - 31000}{13 - 12} \).

Step3: Calculate numerator and denominator

First, calculate the numerator: \( 32500 - 31000 = 1500 \). Then, calculate the denominator: \( 13 - 12 = 1 \).

Step4: Find the slope

Divide the numerator by the denominator: \( m=\frac{1500}{1}=1500 \).

Answer:

1500