Final answer:
The student's question relates to establishing a linear relationship between study hours and exam grades in Mathematics. Each linear equation option suggests a different base exam grade (intercept) and a consistent benefit of studying (slope), where each hour of study is predicted to increase the exam grade by 2 points.
Step-by-step explanation:
The student is asking a question related to Mathematics, specifically, the application of linear regression to predict outcomes. The question involves determining whether there is a relationship between the number of hours studied, s, and the exam grade received, y. The options provided are different linear equations, suggesting that the exam grade depends linearly on the number of hours studied. Each option represents a different linear model with its own y-intercept, indicating the grade one would receive without studying (s=0).
To determine if it pays to study for an exam, one can look at the slope of the equation, which in every given option is 2. This implies that for every additional hour of studying, the exam grade increases by 2 points. The intercept varies from 70 to 90, which could represent the base exam grade one might achieve without any studying. As such, option A corresponds to a base grade of 70, B to 75, C to 90, and D to 85, respectively.
The table provided, although not directly related to the student's question, implies that real-world data can be used to create such regression equations. The regression equation allows us to predict the exam score based on the number of hours studied. For example, using option A, if a student studies for 10 hours, the predicted exam grade would be y = 2(10) + 70 = 90.