A chemical reaction occurs when a solution heated Following

A chemical reaction occurs when a solution heated. Following the reaction, students observe qualities of the solution it cools. The temperature is recorded every five minutes. Find the most appropriate regression equation given the following data. a. Y = -2.96x + 78.4 b. Y = .14x^3 - 7.23x + 96.17 c. Y = 99.8* .90* d. Y = -.005x^3 + .35x^2 - 9.58

Solution

To determine the most appropriate regression equation, we need to fill up the following table.

Time (min)

Temp(F⁰)

Temp(F⁰) as per (a)              -2.96x+78.4

Temp(F⁰) as per (b)

0.14x²-7.23x+96.17

Temp(F⁰) as per (c)

99.8*0.90^x

Temp(F⁰) as per (d)

-0.005x³+0.35x²-9.58

0

100.1

78.4

96.17

99.8

-9.58

5

59.1

63.6

63.52

58.93

-1.455

10

34.8

48.8

37.87

34.80

20.42

15

20.5

34

19.22

20.55

52.295

20

12.2

19.2

7.57

12.13

90.42

25

7.1

4.4

2.92

7.16

131.045

30

4.3

-10.4

5.27

4.23

170.42

It is apparent that the formula as per option (b) i.e. 99.8*0.90^x is the most appropriate regression equation.

Time (min)	Temp(F0)	Temp(F0) as per (a)              -2.96x+78.4	Temp(F0) as per (b) 0.14x2-7.23x+96.17	Temp(F0) as per (c) 99.8*0.90x	Temp(F0) as per (d) -0.005x3+0.35x2-9.58
0	100.1	78.4	96.17	99.8	-9.58
5	59.1	63.6	63.52	58.93	-1.455
10	34.8	48.8	37.87	34.80	20.42
15	20.5	34	19.22	20.55	52.295
20	12.2	19.2	7.57	12.13	90.42
25	7.1	4.4	2.92	7.16	131.045
30	4.3	-10.4	5.27	4.23	170.42