A STAT 200 instructor believes that the average quiz score is a good predictor o

Question

A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final exam score.

(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

(b) Based on the equation from part (a), what is the predicted final exam score if the average quiz score is 90? Show all work and justify your answer.

x 80 93 50 60 100 40 85 70 75 85 y 72 95 75 68 90 35 83 60 77 85

Explanation / Answer

a.

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=738 , Y=740 , XY=57080 , X2=57724

Step 3: Use the following equations to find a and b:

a=YX2XXYn/X2(X)2=7405772473857080/1057724738218.122

b=nXYXY/nX2(X)2=1057080738740/1057724(738)20.757

Step 4: Substitute a and b in regression equation formula

y = a + bx= 18.122 + 0.757x

b. for x=90, y=86.252

X Y XY XX 80 72 5760 6400 93 95 8835 8649 50 75 3750 2500 60 68 4080 3600 100 90 9000 10000 40 35 1400 1600 85 83 7055 7225 70 60 4200 4900 75 77 5775 5625 85 85 7225 7225

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.