Suppose a midterm consits of 10 questions Each question is m

Suppose a midterm consits of 10 questions. Each question is marked either right or wrong. If an answer is right, it recieve +2 points. If it is wrong it recieves -0.5 points.

(b) For the students who took the midterm, the average number of cups of coffee in the week before the midterm is 6, with an SD of 2. The average midterm score is 13, with an SD of 3. The correlation between cups of coffee and midterm scores is -0.2. The scatter plot is football-shaped. Find the equation for the regression line predicting midterm score from number of cups of coffee drank the week before the midterm.

(c) One student drinks 3 cups of coffee more than another student during the week before the midterm. The student that drinks more coffee should be predicted to have a midterm score of about ______ points higher/lower than the other student. If possible fill in the blank and circle either higher or lower. If not possible, explain why not.

Solution

Given that X = 6      Y = 13     _X = 2     _Y = 3    r = -0.2

(b) The regression line of y   on x is given by

(Y- Y) = b_yx (X -   X)

(Y- Y) = r(_X /_Y ) (X -   X)

(Y- 13) = (-0.2)(3 /2 ) (X -   6)

(Y- 13) = (-0.3) (X -   6)

Y = (-0.3) X +14.8