In the linear regression equation $\mathrm{performance}=9.32+0.52\times \mathrm{aptitude score}$, what is the value of the slope?

• A. $1.00$
• B. $0.09$
• C. $9.32$
• D. $0.52$

Answer: (D)

Verified step by step guidance

1. Identify the general form of a simple linear regression equation, which is given by \(y = b_0 + b_1 x\), where \(b_0\) is the intercept and \(b_1\) is the slope.
2. In the given equation, performance = 9.32 + 0.52 × aptitude score, recognize that 9.32 corresponds to the intercept \(b_0\) and 0.52 corresponds to the slope \(b_1\).
3. Understand that the slope \(b_1\) represents the change in the dependent variable (performance) for each one-unit increase in the independent variable (aptitude score).
4. Therefore, the value of the slope is the coefficient multiplying the aptitude score, which is 0.52 in this equation.
5. Conclude that the slope of the regression line is 0.52, indicating how performance changes with aptitude score.