XR19-13 The manager of a company that manufactures plasterboard wants to analyse the factors that…

XR19-13 The manager of a company that
manufactures plasterboard wants to analyse the factors that affect demand for
his product. Plasterboard is used to construct walls in houses and offices.
Consequently, the manager decides to develop a regression model in which the
dependent variable is monthly sales of plasterboard (in hundreds of 4 × 8
sheets) and the independent variables are:

• number of building permits used in the
state

• five-year mortgage rates (in percentage
points)

• vacancy rate in apartments (in percentage
points)

• vacancy rate in office buildings (in
percentage
»

XR19-13 The manager of a company that
manufactures plasterboard wants to analyse the factors that affect demand for
his product. Plasterboard is used to construct walls in houses and offices.
Consequently, the manager decides to develop a regression model in which the
dependent variable is monthly sales of plasterboard (in hundreds of 4 × 8
sheets) and the independent variables are:

• number of building permits used in the
state

• five-year mortgage rates (in percentage
points)

• vacancy rate in apartments (in percentage
points)

• vacancy rate in office buildings (in
percentage points). To estimate a multiple regression model, he took the
monthly observations from the past two years. The data are recorded in columns
1 to 5 respectively. A computer was used to produce the output below:

a What is the standard error of estimate?
Can you use this statistic to assess the fitness of the model? If so, how?

b What is the coefficient of determination,
and what does it tell you about the regression model?

c What is the coefficient of determination,
adjusted for degrees of freedom? What do this statistic and the statistic
referred to in part (b) tell you about how well this model fits the data?

d Test the overall utility of the model.
What does the p-value of the test statistic tell you?

e Interpret each of the coefficients.

f Test to determine whether each of the
independent variables is linearly related to plasterboard demand.

g Which independent variable appears to be
the best predictor of plasterboard demand? Explain.

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