A statistics professor assigned various grades during the semester including a m
ID: 3223336 • Letter: A
Question
A statistics professor assigned various grades during the semester including a midterm exam and a logistic regression project The prediction equation below was fit, using data from 24 students in the class, to predict the final exam score based on the midterm and project grades: bar Final = 11.0 + 0.53 Midterm + 1.20. Project. a. What would this tell you about a student who got perfect scores on the midterm and project? b. Michael got a grade of 87 on his midterm, 21 on the project, and an 80 on the final. Compute his residual and write a sentence to explain what that value means in Michael's case. Does the prediction equation for final exam scores in Exercise 3.1 suggest that the project score has a stronger relationship with the final exam than the midterm exam? Explain why or why not.Explanation / Answer
Q.3.1 (a) Final score when midterm score is 100 out of 100 and project score 30 out of 30.
Final Score = 11 + 0..53 midterm + 1.20 * project
= 11 + 0.53 * 100 + 1.20 * 30 = 100
(b) Predicted final score when Mid term marks are 87, project score 21
Final score ( predicted) = 11 + 0..53 midterm + 1.20 * project = 11 + 0.53 * 87 + 1.20 * 21 = 82.31 marks
Residual = observed vaalue - predicted value = 80 - 82.31 = -2.31
It means that Michael has got less score in final with respect to with respect to class performance.
Q.3.2 No, The equation doesn't suggest that the project score has a stronger relationship than the midterm score just on the basis of their slope coefficient. Correlation coefficient has different meaning than what is slope. The value of B1 and B2 just tell how much increase or decrease occur in final score with one unit change in independent variable. If we reduce midterm score by 1/10, its B1 will increase ten times. So, we can't say exactly from the equation that which variable has more stronger relationship with the final score.
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