Question

Consider the following regression where gr, is the grade (between 0 and 100) on the final exam for student i and hi is the number of hours studied for the exam in the final week. a) Can you think of another variable that you would like to include in the regression to explain the final grade? b) What is the interpretation of Bo? c) Would you be surprised if you estimated a regression and found that Bi was negative? Explain ) The cntimated regresion looks like this gri 474 1.1h, What is the predicted result of a student that studies 35 hours in the final week for the exam? e) Intercepts do not always have an interpretation that makes sense. Do you think that the value 47 makes sense?

Answer 1

Solution

Back-up Theory

In the estimated regression of Y on X given by: Y = β_0cap + β_1capX,

β_0cap represents the y-intercept mathematically and physically represents the expected value of the response (dependent) variable when the predictor (independent) variable is zero ……............................................................................………(1)

β_1cap represents the slope of the regression line mathematically and physically represents the expected change (increase/decrease) in value of the response (dependent) variable when the predictor (independent) variable changes (increases/decreases) by one unit…………….…............................................................................................................. .. (2)

Now to work out the solution,

Part (a)

Number of class room sessions attended by the student could be a dominant variable impacting the exam score. Answer

Part (b)

β₀ in the given case, represents the intercept and so Vide (1), it would represent the score when the student does not study during the final week for the exam.Answer

Part (c)

Although with more number of study hours, score should be increasing in general (meaning a positive β₁), studying more number of hours than what the student can absorb, could also be detrimental and as such it would not be surprising if β₁ turns out to be negative in some specific cases. Answer

Part (d)

Substituting hi = 35 in the given regression equation, the predicted result would be: 85.5 Answer

Part (e)

Vide (1), intercept β₀ in the given case, represents the score when the student does not study during the final week for the exam and that does make some sense. So the expected score of a student who does not study during the final week for the exam is 47.Answer

DONE