Question

Using the accompanying Student Grades​ data, construct a scatter chart for midterm versus final exam grades and add a linear trendline. What is the​ model? If a student scores 7878 on the​ midterm, what would you predict her grade on the final exam to​ be?

Student	Midterm	Final Exam
1	75	64
2	85	91
3	80	68
4	88	83
5	76	60
6	67	80
7	78	74
8	95	94
9	67	61
10	93	87
11	79	53
12	86	82
13	87	56
14	62	73
15	93	86
16	75	90
17	68	81
18	91	93
19	79	79
20	61	70
21	69	83
22	70	73
23	60	75
24	69	55
25	75	93
26	73	78
27	100	90
28	57	53
29	83	77
30	72	82
31	78	70
32	96	98
33	71	93
34	72	81
35	71	81
36	95	96
37	72	62
38	89	83
39	93	96
40	86	90
41	60	73
42	65	92
43	96	84
44	82	86
45	89	99
46	92	96
47	79	92
48	86	94
49	90	78
50	74	81
51	96	99
52	80	73
53	61	79
54	69	75
55	86	91
56	88	96

What is the model for the​ trendline?

Final Exam Grade= ?+?×Midterm Grade

If a student scores 78 on the​ midterm, her predicted final exam grade would be?

Answer 1

From the given data, scatter plot of midterm grades vs final term grades is as follows-

From the above scatter plot, regression model obtained is simple regression model as there is only one regressor. Model for trendline is y = 0.5973x + 33.51 i.e. Final grades = 0.5973x(Midterm grades) + 33.51.

Now, we have to predict final exam grades, if student scores 7878 on the midterm -

Hence, from the above equation -

Final grades = 0.5973x(Midterm grades) + 33.51

= 0.5973*7878 + 33.51

= 4739.039

4739.039 will be the final score if student scored 7878 at midterm.

If student scores 78 on the mid term then final score will be -

Final grades = 0.5973x(Midterm grades) + 33.51

= 0.5973*78 + 33.51

= 80.0994

80.0994 will be the final score if student scored 78 at midterm.