Final answer:
The correct answer is (a): When perfect multicollinearity is detected in a linear regression model, one of the collinear variables should be removed. Assumption 2 of linear regression requires no perfect multicollinearity among explanatory variables. Removing one variable maintains model integrity without losing vital information.
Step-by-step explanation:
The correct statement about Assumption 2 in linear regression is a. When we spot perfect multicollinearity in our model, we should remove one of the two predictor variables involved. The reason behind this action is that having two or more variables that are perfectly correlated (multicollinearity) can distort the results of regression analysis, making coefficients unreliable and the model unstable. Assumption 2 of linear regression requires that there should be no perfect multicollinearity among explanatory variables. Removing one variable reduces redundancy without losing essential information.
In the context of a linear relationship between variables, the dependent variable is the outcome we are trying to predict or explain, whereas the independent variables are the predictors or factors that we believe have an effect on the dependent variable. We often visualize these relationships using a scatter plot, which can help us identify whether there is a potential linear relationship between the variables.
To quantify the strength of this relationship, we calculate the correlation coefficient (r), which indicates how strongly two variables are related. A value of r = 1 or r = -1 indicates perfect positive or negative correlation, respectively, but it doesn’t necessarily mean perfect multicollinearity in the context of regression with multiple predictor variables. We typically use regression analysis to find the line of best fit and calculate its equation (ý = a + bx), which allows us to make predictions about the dependent variable based on different values of the independent variable(s).
The significance of the correlation coefficient shows how likely it is that the observed relationship in the sample exists in the larger population. If the correlation coefficient is significant, it provides evidence of a linear relationship between x and y in the population.