Consider the following assumptions of regression analysis:

(a) The values of the dependent variable are normally distributed.
(b) The values of residuals have a skewed distribution.
(c) The variance of the dependent variable is constant for all values of the independent variable.
(d) The values of the residuals are independent of each other.

Choose the correct answer from the options given below:

Correct option is C

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The values of the dependent variable are normally distributed. → Correct

• One of the common assumptions in linear regression is that the dependent variable (Y) should be normally distributed for any given value of the independent variable (X).
• This helps in valid hypothesis testing and confidence interval estimation.

The variance of the dependent variable is constant for all values of the independent variable. → Correct

• This refers to the assumption of homoscedasticity, meaning that the variance of residuals remains constant across all levels of the independent variable.
• If this condition is violated, it leads to heteroscedasticity, which affects the efficiency of estimates.

The values of the residuals are independent of each other. → Correct

• This assumption ensures that there is no autocorrelation in the residuals.
• If residuals are dependent, it means serial correlation exists, which is a violation seen in time series data.

​Information Booster:​

If residuals have a skewed distribution, it violates normality, leading to biased estimates.

Heteroscedasticity causes inefficient estimates and affects hypothesis testing.

Autocorrelation leads to misleading conclusions in time-series regression models.

• 1. Linearity: The relationship between the dependent and independent variable must be linear.
  2. Independence: Residuals (errors) should be independent of each other (no autocorrelation).
  3. Homoscedasticity: The variance of residuals should be constant across all levels of the independent variable.
  4. Normality of residuals: The residuals should be normally distributed.
  5. No multicollinearity: Independent variables should not be highly correlated.

Additional knowledge: 

1. (b) The values of residuals have a skewed distribution.→Incorrect

   • One of the commonassumptions in linear regressionis that the dependent variable (Y) should be normally distributedfor any given value of the independent variable (X).
   • This helps invalid hypothesis testingand confidence interval estimation.