Need help solving **Question:**What are the assumptions made about the random error ε in the probabilistic model \( y = \alpha + \beta x + \epsilon \)? (Select the three statements that are correct.)**Options:**- [ ] The values of ε have a Student's t probability distribution.- [ ] The values of ε have a mean of 0 and a constant variance equal for all values of x.- [ ] The values of ε have a mean of 1 and possibly different variances.- [ ] The values of ε have a n degrees of freedom.- [ ] The values of ε are dependent.- [ ] The values of ε have a negative correlation.- [ ] The values of ε have a n - 1 degrees of freedom.- [ ] The values of ε have a positive correlation.- [ ] The values of ε are independent.- [ ] The values of ε have a normal probability distribution.

The probabilistic model is given as follows:Where, is the random error.The following assumptions made about the random error are correct:The values of have a mean of 0 and a constant variance equal for all values of .The values of are independent.The values of have a normal probability distribution.Explanation:The assumptions usually made about the errors in the linear regression model are that they follow a normal distribution with a mean of , have constant variance (homoscedasticity).Also, they are independent of each other and have a mean of 0 with a common variance (constant variance).The following assumptions made about the random error are incorrect:The values of have a student's probability distribution.The values of have a mean of and possibly different variances.The values of have a degrees of freedom.The values of are dependent.The values of have a negative correlation.The values of have a degrees of freedom.The values of have a positive correlation.Explanation:The all above assumptions about the random error are incorrect because the errors follow a normal distribution with a mean of and constant variance. Also, the degrees of freedom in the context of errors typically refer to . The errors are independent of each other and not correlated. A positive or negative correlation between errors violates this assumption.The following assumptions made about the random error are correct:The values of have a mean of 0 and a constant variance equal for all values of .The values of are independent.The values of have a normal probability distribution.