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Question #1
Based on
this
data on the experience (in years) and salary (in thousands of dollars) of
51 employees of a firm, answer the following questions using your results of the
sample linear regression of salary (dependent variable) on experience (independent
variable) and the corresponding residual plot.
1.
The scatterplot of salary on experience suggests that there is
A positive curve
linear relationship
between salary and experience.
2.
Which one of the following seems to be an accurate representation of the
residual plot.
An Ushaped band.
3.
The residual plots of regressing experience (dependent variable) on salary
(independent variable) will
be the opposite of the residual plot from a
regression of salary on experience and exhibit an invertedU shape band.
4.
The value of R?you obtain from this regression is
0.784507379 =
0.784507379
5.
Now add an additional independent variable, called "experience2". Create this
variable by squaring all the values of experience and entering them in to a new
column. Now run a multiple regression with experience and experience2 as
your independent variables, keeping salary as your dependent variable. (This
is defining a curvilinear relationship between salary and experience.) In this
case, the value for R?is
0.963849893
Question #2
A general manager at a supermarket chain believes that sales of a product are
influenced by the amount of space the product is alloted on shelves. If true, this would
have great significance, because the more profitable items could be given more shelf
space. The manager realizes that sales volume would likely increase with more space
up to a certain point. Beyond that point, sales would likely flatten and perhaps
decrease (because customers often are dismayed by very large exhibits). To test his
belief, the manager records the number of boxes of detergent sold during 1 week in 25
stores in the chain. For each store, he records the shelf space (in inches) alloted to the
detergent. The data is stored
here
.
1.
The scatterplot of SALES on SPACE suggests that there is
a negative curve
linear relationship
between SALES and SPACE.
2.
Run a regression with SALES as your dependent variable and SPACE as your
independent variable. The adjusted R
2
is
0.015210895
, while the pvalue
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View Full Documentfor the overall Ftest is
0.431751675
, indicating that at the 5% level of
significance, the linear model is
not valid
.
3.
Now, since the inital scatterplot suggested a nonlinear relationship between
SALES and SPACE, it was expected that the linear model would not be a
good fit. Now create an additional independent variable calles SPACE2, which
is going to take squared values of the SPACE column and run a regression
with two independent variables (SPACE and SPACE2). The adjusted R
2
is
0.352828885
, while the pvalue for the overall Ftest is
0.003202847
,
indicating that at the 5% leve of significance, the quadratic model is
valid
.
Looking at the two independent variables, you can say that at the 10% level of
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 Spring '09
 PETRY

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