For each problem, determine the appropriate statistical analysis to answer the objective. Justify and construct the proposed formula or model and define each component $.$ State all the necessary assumptions for inferential analysis to be valid.

a$.$ You want to examine the relationship between the amount of time spent studying and the students' exam scores. However, there is a potential confounding variable, such as the number of hours of sleep the night before the exam and failing to account for the effect of sleep hours could lead to a misinterpretation of the relationship between study time and exam scores.

b$.$ You want to predict a person's salary based on their years of experience, level of education, and age. It is known that they for a multivariate distribution. You want to select a random sample of working persons in your village and obtain the necessary data.