Question

1. The grades of five students in mathematics and chemistry classes are:

2. x = Mathematics	6	4	8	5	3.5
   y = Chemistry	6.5	4.5	7	5	4

   1. Compute the correlation coefficient. (2 decimal places)
   2. Determine the regression line equation. (2 decimal places)
   3. Calculate the expected grade in chemistry for a student who has a 7.5 in mathematics.
   4. According to your model, if a student got a 7 in chemistry, what should the students mathematicsgrade have been? (nearest tenth)

Answer 1

X	Y	XY	X^2	Y^2
6	6.5	39	36	42.25
4	4.5	18	16	20.25
8	7	56	64	49
5	5	25	25	25
3.5	4	14	12.25	16

From the above table and formula we get the value are as:

n	5
sum(XY)	152.00
sum(X)	26.50
sum(Y)	27.00
sum(X^2)	153.25
sum(Y^2)	152.50
Numerator	44.50
Denominator	46.30
r	0.9611

the correlation coefficient. = 0.96

From the above table and formula we get the value are as:

n	5
sum(XY)	152.00
sum(X)	26.50
sum(Y)	27.00
sum(X^2)	153.25
sum(Y^2)	152.50

b	0.6953
a	1.7148

Regression line equation are as:

y = a + bx

y = 1.71 + 0.70x

when x = 7.5

y = 1.71 + 0.70 * 7.5

y = 6.96

Expected grade in chemistry = 6.96

when y = 7

y = 1.71 + 0.70x

7 = 1.71 + 0.70x

0.70x =6.71

x = 9.59