Question

In any regression model, p denotes the number of explanatory variables in the model. In simple linear regression (SLR),

p=1. True/False?

When testing whether the slope of a explanatory variable is 0 or not in context of multiple regression, what distribution is used to determine the p-value? standard normal distribution / t distribution with n−1 degrees of freedom / t distribution with n−2 degrees of freedom / t distribution with n−p−1 degrees of freedom ?

In multiple regression, there is always a single residual plot which can help you verify all model assumptions. True/ False?

If a variable is not significant in a multiple regression model, it will also not be significant in a simple regression model. True/ False?

When the errors show a non-random pattern in a residual plot, that means that your model probably is not appropriate for linear regression. True/ False?

Answer 1

Q.1 True

(Since, in simple linear regression there is only one explanatory variable hence p=1 in SLR )

Q.2 t-distribution with n-p-1 degrees of freedom

(Test for significance of regression coefficient, test statistic follows t with n-p-1)

Q.3 True

(Multiple regression has single residual plot to verify assumption of model it doesn't matter how many explanatory variables in model)

Q.4 True

Q.5 True

(Since, assumption of constant error variance violeted due to nonrandom pattern in residual plot and such model is not appropriate)