Review for inclass portion of Test #3
(The takehome problem will involve using Excel to perform a regression analysis.)
1
. Translate the team’s belief below into a model specification.
Then indicate the signs of the model
coefficients consistent with the team’s belief.
An executive team for a chain of pharmacies gathered the following data on its existing pharmacies:
Sales =
dollar sales last quarter
Pop = (estimated) number of people residing within ten miles of the pharmacy
PCI = (estimated) per capita income of population within ten miles of the pharmacy
Competitors = number of competitors within two miles of the pharmacy
HighSchool = 1 if a high school is within one mile of the pharmacy, 0 otherwise
The team believes that:
•
Sales increases with PCI in a diminishing returns sense
•
Sales are higher in a pharmacy with a high school within one mile than in a pharmacy without a high school
within one mile
•
Sales increases with Pop
•
Sales decreases with the number of competitors
2
. The manager of a deliveryonly pizza establishment wanted to assess the relationship between the time
(in minutes) to travel to a customer’s residence and the distance (in miles) to the residence.
For a
random sample of 30 deliveries (of pizza to customer residences over the past month), the travel time
and distance were recorded.
The enclosed Excel sheet labeled
Pizza Delivery scenario
contains the
results of a regression analysis on the sample data using a model specification of Time = β
0
+
β
1
Distance + ε.
Note
:
Using 2 decimal places is adequate.
[source: Adapted from Weiers (2008)]
(a)
Graph (on the scatter diagram on the Excel sheet) the sample regression equation/line, being
sure to specify (on or near the scatter diagram) two of the points on the line.
(b)
Based on the residual plot:
Does the linearity assumption appear met?
Does the equal variances
assumption appear met?
Does the normality assumption appear met?
Assume henceforth that all model assumptions are adequately met.
(c)
Use the pvalue approach to hypothesis testing to test H
0
: β
1
= 0
(d)
Predict the time to travel to a residence 4.5 miles from the establishment.
(e)
Interpret the standard error of the estimate.
(f)
Interpret 1.68, the sample regression coefficient of Distance.
(g)
Suggest a variable besides Distance that could assist in predicting delivery time.
(h)
If the variable you suggested in (g) does indeed assist in predicting delivery time when used
along with distance, what would you expect to happen to R
2
and what would you expect to
happen to the standard error of the estimate if you gathered data on that variable and then reran
the regression, this time regressing Time on Distance and that variable?
3
. A realty that sells homes along the east coast of the United States hopes to develop some guidelines
regarding heating costs for single family homes.
For a random sample of 20 homes along the east
coast, the company determined:
Cost = the heating cost (in $) last January;
Temperature = the mean outside temperature (in degrees Fahrenheit) last January; and
Insulation = the number of inches of insulation in the attic.
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 Fall '08
 STAFF
 Statistics, Regression Analysis, Standard Error, Statistical hypothesis testing, Errors and residuals in statistics, R Square

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