1. Consider the simple linear regression model Y₁ = a + BX; + u₁, where i denotes an observation, Y and X is the outcome explanatory variables and u is the error term. a. Suppose Y denotes GPA and X denotes study hours per week. Suppose that the relationship between study hours and GPA is deterministic. Specifically, if you do not study your GPA for sure will be a miserable 0.3. And, for every hour you study, your GPA will for sure increase by 0.25 points. Write the equation for this deterministic relationship. And, plot GPA conditional on study hours, where these hours runs from 0 to 16 on the X-axis. Why is ui always equal to 0? b. Why is this deterministic relationship a completely unrealistic view of reality? C. Illustrate on your figure random errors, u₁, that are positive shocks indicating that the deterministic model underpredicts the GPA. And illustrate random errors that are negative shocks indicating the model overpredicts. d. The linear model illustrated in diagram is GPA = a + ß* Hours-Studied + u. What does it mean that Hours-Studied are orthogonal to u? e. How is 3 estimated? f. Explain why an estimator of ß can only be accurate (unbiased) when E(u₁|x₁) = 0?

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