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

a. A slope close to 0

b. A correlation coefficient close to 0

c. A slope close to - 1

d. A correlation coefficient close to - 1

Answer - B. (A correlation coefficient close to 0)

When the correlation coefficient of a data set is close to zero (0), this makes a linear regression model unreasonable. The typical linear regression model is characterized by the following conditions:

1. The regression function is linear with constant but unknown coefficients.

2. The expected value of the disturbance term is zero.

3. The disturbance terms have a constant variance (homoscedasticity).

4. The disturbance terms are uncorrelated with each other.

If any of these 4 conditions is not met, then the linear regression model would become unreasonable.