Students in a science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:

Student	1	2	3	4	5	6	7	8	9
1st Test Grade	99	78	89	81	97	62	67	96	70
Final Average	92	77	83	72	83	63	63	94	75

You are also provided the results from several different linear regression relationships for the above data. These provide different regression relationships looking at different combination of independent and dependent variables.

Regression Relationship	Independent variable	Dependent variable		Value of b Slope		Value of a (y-intercept		Coefficient of determination, r2
Regression1	Student	Final Ave		-1.13		83.78		0.073
Regression2	Final Ave	1st Test grade		1.11		-4.35		0.831
Regression3	Student	1st Test grade		-2.18		92.92		0.183
Regression4	1st Test grade	Final Ave		0.75		16.51		0.831
Regression5	Final Ave	Student		0.066		10.16		0.073

a. (5 points) Provide the linear regression equation that can be used to predict the final course average based on the first test grade.

A.	83.78+-1.13 *(First Test Grade)

)

B.	16.51+0.75 *(First Test Grade)

C.

92.92+-2.18 *(First Test Grade)

0

D.

-4.35+1.11*(First Test Grade)

b. (5 points) Predict the final average of a student who made an 86 on the first test.

A.

81.01

B.

82.89

C.

79.33

D.

85.43

c. (5 points) Would you recommend using this relationship for forecasting the final averages?

A. Recommend

==

B.	Not Recommend

d. (5 points) Suppose a student scored a 38 on the first test. Predict the final average of a student who had this score? Valid forecast or not?

A.	51.33, not valid outside range of known values

,,

B.

43.56, valid

C.	45.01, not valid outside range of known values

,

D.	55.67, valid