Question

which characteristic of a data set makes a linear regression model unreasonable?

a slope close to 0
a correlation coefficient close to 0
a slope close to -1
a correlation coefficient close to -1

Explanation:

Analyze the meaning of the correlation coefficient

$$ r \in [-1, 1] $$

Evaluate the strength of linear relationship based on \(r\)

$$
LATEXBLOCK0
$$

Determine the condition for an unreasonable linear model

$$ r \approx 0 \implies \text{Linear regression model is unreasonable} $$

Answer:

• a slope close to 0
• a correlation coefficient close to 0 (Correct answer)
• a slope close to \(-1\)
• a correlation coefficient close to \(-1\)