Which one of the following statements is false?

Correct option is C

Regression coefficient of the two variables may have different algebraic symbols for real-life situations is false.
Regression is a statistical technique used to analyze the relationship between a dependent variable and one or more independent variables. The properties of regression include:
1. Linearity: The relationship between the dependent variable and independent variable(s) should be linear. This means that the relationship between the two variables can be approximated by a straight line.
2. Independence: The observations used in regression should be independent of each other. This means that the value of one observation should not be influenced by the value of another observation.
3. Homoscedasticity: The variance of the errors (residuals) should be constant across all levels of the independent variable(s). This means that the spread of the residuals should not vary with the level of the independent variable(s).
4. Normality: The errors (residuals) should be normally distributed. This means that the distribution of the residuals should be bell-shaped and centered around zero.
5. Multicollinearity: If there are multiple independent variables in the regression model, they should not be highly correlated with each other. High levels of correlation between independent variables can lead to unstable estimates of the regression coefficients.
6. Outliers: The presence of outliers can have a significant impact on the regression results. Outliers are data points that are significantly different from the other data points and can have a large influence on the regression model.
Hence options (a), (b) and (d) are correct and option (c) is not correct as the Regression coefficient of the two variables may have the same algebraic symbols for real-life situations.