Question

Q1. An experiment has been performed to determine the steady-state power delivered by a gas turbine driven generator as a function of fuel flow rate. The following normalized data were obtained: Fuel Flow Rate Power Generated $u_i$ $Y_i$ 1.0 2.0 2.3 4.4 2.9 5.4 4.0 7.5 4.9 9.1 5.8 10.8 6.5 12.3 7.7 14.3 8.4 15.8 9.0 16.8 (a) Plot $u_i$ versus $Y_i$. Add appropriate plot title and axis labels. (b) Create a matrix X, where the first column contains ones and the second column is $u_i$. (c) Create a matrix Y with one column contains $Y_i$. (d) The model predictions for the data in the above table are given by the following regression model: $\hat{Y} = X\beta$, where $\beta$ is given by $\beta = (X^TX)^{-1}X^TY$. Calculate $\beta$. (e) Calculate $\hat{Y}$ (f) Plot $u_i$ versus Y and $u_i$ versus $\hat{Y}$ on the same figure. Add appropriate plot title, axis labels and legend. Use red 'o' for Y and blue line for $\hat{Y}$. (g) Calculate mean square error (mse) given by: mse=$e^Te$/n where $e = \hat{Y} - Y$ and n is the number of data points. (h) Plot e versus $\hat{Y}$. Add appropriate plot title and axis labels.

          Q1. An experiment has been performed to determine the steady-state power delivered by a
gas turbine driven generator as a function of fuel flow rate. The following normalized data
were obtained:
Fuel Flow Rate Power Generated
$u_i$	$Y_i$
1.0	2.0
2.3	4.4
2.9	5.4
4.0	7.5
4.9	9.1
5.8	10.8
6.5	12.3
7.7	14.3
8.4	15.8
9.0	16.8
(a) Plot $u_i$ versus $Y_i$. Add appropriate plot title and axis labels.
(b) Create a matrix X, where the first column contains ones and the second column is $u_i$.
(c) Create a matrix Y with one column contains $Y_i$.
(d) The model predictions for the data in the above table are given by the following
regression model: $\hat{Y} = X\beta$, where $\beta$ is given by $\beta = (X^TX)^{-1}X^TY$. Calculate $\beta$.
(e) Calculate $\hat{Y}$
(f) Plot $u_i$ versus Y and $u_i$ versus $\hat{Y}$ on the same figure. Add appropriate plot title, axis
labels and legend. Use red 'o' for Y and blue line for $\hat{Y}$.
(g) Calculate mean square error (mse) given by:
mse=$e^Te$/n
where $e = \hat{Y} - Y$ and n is the number of data points.
(h) Plot e versus $\hat{Y}$. Add appropriate plot title and axis labels.

Q1. An experiment has been performed to determine the steady-state power delivered by a
gas turbine driven generator as a function of fuel flow rate. The following normalized data
were obtained:
Fuel Flow Rate Power Generated
ui Yi
1.0 2.0
2.3 4.4
2.9 5.4
4.0 7.5
4.9 9.1
5.8 10.8
6.5 12.3
7.7 14.3
8.4 15.8
9.0 16.8
(a) Plot ui versus Yi. Add appropriate plot title and axis labels.
(b) Create a matrix X, where the first column contains ones and the second column is ui.
(c) Create a matrix Y with one column contains Yi.
(d) The model predictions for the data in the above table are given by the following
regression model: Ŷ = Xβ, where β is given by β = (X^TX)^-1X^TY. Calculate β.
(e) Calculate Ŷ
(f) Plot ui versus Y and ui versus Ŷ on the same figure. Add appropriate plot title, axis
labels and legend. Use red 'o' for Y and blue line for Ŷ.
(g) Calculate mean square error (mse) given by:
mse=e^Te/n
where e = Ŷ - Y and n is the number of data points.
(h) Plot e versus Ŷ. Add appropriate plot title and axis labels.

Added by Andrew F.

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