Whether the parameters of simple linear regression model beta0(intercept) and beta1(slope) are unbiased? I was taught that these are unbiased estimators in my college. But one of my friends is telling that they are not unbiased. I will be grateful if I get a proper solution
Unbiased are not guaranteed in linear regression. The most common cause is incorrect model specification.
Assume there is non-zero correlation between $X_1$ and $X_2$. Assume your true model is $Y = b_1X1 + b_2X2 + e$ in a standard OLS regression framework.
If you miss out the important $X_2$ predictor, the residuals are forced to "eat" the missing effects from $X_2$. In statistics, we say the residuals are no longer uncorrelated to $X_1$.
This is known as Omitted-variable bias. Thus, neither yourself nor your friend is wrong.
At first, need to distinguish the parameters and their estimate. In your question, intercept and parameter are parameter as you stated. They are existed constant, but we do not know. Just like your age. It exist, but I do not know. And also your age cannot be wrong. Same as parameters, they are unknown constant and cannot be biased or unbiased.
Based on the data, we can guess the parameters by some mathematical skills. The methods of guess is called estimate. One property of the estimate is un/biased. It is possible that your college and you friend talked about different estimate of the intercept and slope. You did not mention the estimate they talked about, so no one can give you the answer.