The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature ( x 1 ), the number of days in the month ( x 2 ), the average product purity ( x...

The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x₁
), the number of days in the month (x
₂), the average product purity (x
₃), and the tons of product produced (x
₄). The past year’s historical data are available and are presented in the following table 1:

Table 1 : Historical data

(a) Fit a multiple linear regression model to these data.

(20 marks)

(b) Estimates.

(4 marks)

Q2

A study was performed on wear of a bearing
yand its relationship to
x₁

oil viscosity and
x
₂
load. The following data were obtained as shown in table 2.

Table 2 : Bearing data

(a) Fit a multiple linear regression model to these data.

(20 marks)

(b) Estimate s²
and the standard errors of the regression coefficients.

(4 marks)

(c ) Use the model to predict wear when
x₁
= 25
and
x₂
= 1000.

(1 marks)

Q3

An engineer at a semiconductor company wants to model the relationship between the device HFE ( y) and three parameters: Emitter-RS (x₁
), Base-RS (x₂
), and Emitter-to-Base RS (x₃
). The data are shown in the following table 3.

Table 3 : Device parameters data

(a) Fit a multiple linear regression model to the data.

(20 marks)

(b) Estimate s²

(1 mark)

(c) Find the standard errors of the regression coefficients.

(4 marks)

(d) Predict HFE when
x₁=14.5, x₂=220
and
x₃=5.0