Explanation

In time series regression analysis, spurious regression occurs when:

• Both variables have unit roots (are non-stationary)
• The regression appears to show significant relationships when none actually exist
• Standard t-statistics and R² become invalid

Valid scenario (Option B):

• When the dependent variable has a unit root but the independent variable is stationary
• This can produce valid regression results because the stationary independent variable can help explain the non-stationary dependent variable
• The regression may capture a legitimate relationship

Invalid scenario (Option A):

• When both variables have unit roots, the regression is likely spurious
• Standard test statistics become unreliable
• The regression may show high R² and significant coefficients even when no true relationship exists

For valid regression test statistics with time series data, it's generally required that either both variables are stationary, or they are cointegrated if both are non-stationary.