XR19-50 The managing director of a real estate company wanted to know why certain branches of the…

XR19-50 The managing director of a real
estate company wanted to know why certain branches of the company outperformed
others. He felt that the key factors in determining total annual sales (in
$millions) were the advertising budget (in $000s), x1, and the
number of sales agents, x2. To analyse the situation, he took a
sample of 15 offices and ran the data through a statistical software system.
Part of the data and the output are shown below.

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XR19-50 The managing director of a real
estate company wanted to know why certain branches of the company outperformed
others. He felt that the key factors in determining total annual sales (in
$millions) were the advertising budget (in $000s), x1, and the
number of sales agents, x2. To analyse the situation, he took a
sample of 15 offices and ran the data through a statistical software system.
Part of the data and the output are shown below.

a Interpret the coefficients.

b Test to determine whether there is a
linear relationship between each independent variable and the dependent
variable, with _ = 0.05.

c Test the overall utility of the model.

d Interpret the value of R2. The
predicted values and the residuals are as follows:

e Is collinearity a problem?

f Does it appear that the error variable is
normal?

g Does it appear that 2 _ _ is
fixed?

h Does it appear that the errors are
independent?

i Do any of your answers to (e)–(h) cause
you to doubt your answers to (a)–(d)? Suppose that a third independent variable
was included – the average number of years of experience in the real estate
business x3 for each office. These data are as follows:

j What differences do you observe between
this output and the original output? How do you account for any differences?

k The correlation matrix is

Does this explain some of the differences?
Why or why not?

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