Question

X 1 1 2 2 3 3 4 5 6 7 Y 2 7 7 10 8 12 10 14 11 14 Ln(Y) 0.693147 1.94591 1.94591 2.302585 2.079442 2.484907 2.302585 2.639057 2.397895 2.639057 a) Fit the model $Y = ae^{bx}$ to the above data. b) Compute $R^2$ of the above model for the above data. (10+10=20 marks)

          X
1
1
2
2
3
3
4
5
6
7
Y
2
7
7
10
8
12
10
14
11
14
Ln(Y) 0.693147 1.94591 1.94591 2.302585 2.079442 2.484907 2.302585 2.639057 2.397895 2.639057
a) Fit the model $Y = ae^{bx}$ to the above data.
b) Compute $R^2$ of the above model for the above data.
(10+10=20 marks)

X
1
1
2
2
3
3
4
5
6
7
Y
2
7
7
10
8
12
10
14
11
14
Ln(Y) 0.693147 1.94591 1.94591 2.302585 2.079442 2.484907 2.302585 2.639057 2.397895 2.639057
a) Fit the model Y = ae^bx to the above data.
b) Compute R^2 of the above model for the above data.
(10+10=20 marks)

Added by John R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/16/2023

Step 1

To fit the model $Y = ae^{bx}$ to the data points, we need to take the natural logarithm of $Y$ and then perform linear regression on the transformed data. This will give us the values of $a$ and $b$ in the model. Let's denote $\ln(Y)$ as $Y'$ for Show more…

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[ egin{array}{ccccccccccc} X & 1 & 1 & 2 & 2 & 3 & 3 & 4 & 5 & 6 & 7 \ Y & 2 & 7 & 7 & 10 & 8 & 12 & 10 & 14 & 11 & 14 \ ln(Y) & 0.693147 & 1.94591 & 1.94591 & 2.302585 & 2.079442 & 2.484907 & 2.302585 & 2.639057 & 2.397895 & 2.639057 \ end{array} ] a) Fit the model (Y = ae^{bx}) to the above data. b) Compute (R^2) of the above model for the above data.