Final answer:
The correct answer is that for linear regression, the assumption that there is a linear relationship between the independent and dependent variables is essential, meaning a good, linear model is required. Variables' relevancy is key as it affects the relationship and the accuracy of the regression results.
Step-by-step explanation:
The first assumption for linear regression is that there is a linear relationship between the independent and dependent variables. This assumption is crucial to the proper function of the model, meaning that including non-relevant predictor variables (option a) or excluding relevant ones (option b) can misrepresent the relationship and provide inaccurate regression results. Thus, the correct answer is that we need a good, linear model (option d).
To explore the linear relationship, you begin by deciding which variable should be the independent variable and which should be the dependent variable.
Afterward, you draw a scatter plot to visualize the data points. From the scatter plot, you can inspect whether there appears to be a relationship between the variables.
You then calculate the least-squares line, typically represented in the form ŷ = a + bx, and find the correlation coefficient, which helps determine the strength and direction of the linear relationship.
Finally, the significance of the correlation coefficient needs to be interpreted to decide whether the linear model can be considered a good fit for the data, making it possible to make predictions or infer relationships, depending on the result.
If a significant correlation is identified, it implies a linear relationship that can be modeled through regression.