7. [7 points] Suppose you are estimating the effect of mandatory study hall on test performance. You find Score$_i$=52+12Hours$_it$+4Sleep$_it$ for person $i$ at time $t$ where Hours is hours studied and Sleep is hours slept.
(a) [1 points] Is there a positive or negative correlation between hours studied and performance?
(b) [1 points] Is there a positive or negative correlation between hours slept and performance?
(c) [3 points] Suppose you find the correlation between hours slept and hours studied is -0.15. If you omitted hours slept from the equation above, would your estimate for hours studied be biased upwards or downwards? How do you know?
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(d) [2 points] Name two other variables you would like to control for in this scenario. What do you think their correlation is with hours studied? With overall score? How would omitting these variables bias your estimate for hours studied (describe the effect of each)?