Question

1.) You are interested in predicting the final grade of students in a business course. You collect data on the number of hours studied and final grade for 8 students. Using the data provided below, find the predicted linear regression equation. Do this long hand on notebook paper.  You must show all of your calculations. Take calculations out to the 4th decimal place. Do not round up or round down.

Your answers must clearly show your answers for bo, b1, and the predicted linear regression equation.  

Data Definitions:

Student - student identifying number

Hours of study - number of hours studied

Final Grade - based on 0-100 scale

Student	Hours Studying	Final Grade
1	42	92
2	58	95
3	32	81
4	39	78
5	37	75
6	51	88
7	49	85
8	45	85

2.) Using the predicted linear regression equation from #1, find the predicted final grade for a student who studied 40 hours.

4.) Refer back to Question #1, what is another explanatory variable that you could use to predict final grade? Why did you chose this variable? In other words, justify your decision.

Answer 1

(1)

From the given data, the following Table is calculated:

X	Y	XY	X2
42	92	3864	1764
58	95	5510	3364
32	81	2592	1024
39	78	3042	1521
37	75	2775	1369
51	88	4488	2601
49	85	4165	2401
45	85	3825	2025
Total = 353	679	30261	16069

b0 = 58.006

b1 = 0.609

the predicted linear regression equation.  

y = 58.006 + 0.609 x

(2)

For x =40:

y = 58.006 + ( 0.609 X 40)

= 82.366

So,

Answer is:

82.366

(3)

Another explanatory variable that you could use to predict final grade : Student's attentiveness and punctuality in the class.

But, we prefer to consider Hours studying because Hours studying being quantitative is easy to collect data and input in the model directly.

Student's attentiveness and punctuality in the class.being qualitative is difficult to collect data. The same is to be converted to numerical figures and then only the model is applicable.