Question

 

Nine students in a college math class took a pre-test. We are interested in whether the pre-test is useful for predicting final course percentage. Here are the students’ scores: Student 1 2 3 4 5 6 7 8 9 Pre-Test 83 81 70 79 69 61 88 72 86 Final Course Percentage 68 59 72 75 55 52 81 63 70

(a) Use R to make a scatterplot of the data. Does it seem like a straight line model is reasonable?

(b) Use your calculator to find the correlation, r, for these data. (You may use R as a check.)

(c) Assuming a straight-line model, compute estimates of the intercept (β0) and slope (β1). Please do this part with your calculator. (You may use R as a check.)

(d) If a student scores 80 on the pre-test, what does the model predict will be that student’s final score? Please do this part with your calculator. (You may use R as a check.)

Answer 1

(a) data are scattered so it seems straight line is reasonable

(b) r=(n*sum(xy)-sum(x)*sum(y))/sqrt(n*sum(x²)-(sum(x))²)*(n*sum(y²)-(sum(y))²)=0.7056

(c) 0=(sum(y)*sum(x²)-sum(x)*sum(xy))/(n*sum(x²)-(sum(x))²)=8.6029

1=(n*sum(xy)-sum(x)*sum(y))/ (n*sum(x²)-(sum(x))²)=0.7512

s.n.	Pre-test(x)	Final(y)	x2	y2	xy
1	83	68	6889	4624	5644
2	81	59	6561	3481	4779
3	70	72	4900	5184	5040
4	79	75	6241	5625	5925
5	69	55	4761	3025	3795
6	61	52	3721	2704	3172
7	88	81	7744	6561	7128
8	72	63	5184	3969	4536
9	86	70	7396	4900	6020
sum=	689	595	53397	40073	46039

(d)answer is 68.7

if pre-test x=80, the final score y=  0+ 1*x=8.6029+0.7512*80=68.70