Question #1
Look at the example on slide 41 (page 87) of the course packet. They want you to do a test on the correlation coefficient (that is, a test
to see if any linear relationship exists between two variables) between student population size and pizza sales, based on the Armani
Pizza example. The data is provided
here
. Answer the following questions based on your findings.
1.
The sample correlation coefficient between sales in thousands of dollars and the number of students in thousands is given
by
0.963366334
If sales was measured in millions of dollars instead of thousands of dollars then the correlation
coefficient
o
would go down
o
would stay the same
o
would go up
o
cannot be computed
.
2.
Suppose you would like to test whether the population correlation coefficient between number of students and sales is 0.
The value of the test statistic for testing this hypothesis is
10.16004421
and the pvalue is
7.53839E06 = 7.53839e06
.
This test statistic and pvalue are
the same as
the test statistic and pvalue for the test of the regression slope
coefficient. Then, based on these results, you can say that:
a linear relationship does exist
between pizza sales and the
size of student population.
3.
Now do the Ftest for overall validity of the model
(slide 30 on page 84)
. What is the value of the test statistic?
103.2264983
and the corresponding pvalue is
7.53839E06 = 7.53839e06
.
This pvalue is
the same as
the pvalue for the individual ttest of the regression slope coefficient.
You received a raw score of 89% on this question.
Question #2
Look at the example on slide 40 (page 86) of the course packet. Do a test on the correlation coefficient (that is, a test to see if any
linear relationship exists between two variables) between the odometer milage and used car prices, based on the Car Sale Price
example. Partial results are provided
here
. Answer the following questions based on your findings.
1.
The sample correlation coefficient between used car sale price and the odometer mileage is given by
.806 = 0.806
.
2.
Suppose you would like to test whether the population correlation coefficient between odometer mileage and used car price
is 0. The value of the test statistic for testing this hypothesis is
13.49465085
and the pvalue is
4.44346E24 =
4.44346e24
.
3.
Now do the Ftest for overall validity of the model
(slide 30 on page 84)
. What is the value of the test statistic?
182.1056015
. The numerator and denominator degrees of freedom for this Ftest are repectively
1
and
98
. The
corresponding pvalue is
4.44346E24 = 4.44346e24
.
Item 1:
Your answer is within ±0.1% of the solution  correct.
Question #3
It has been a popularly held belief that surfing the web actually reduces your productivity at the workplace. You are appointed by the
manager of HoleinOne, a Swiss cheese distributing company, as a consultant to find out the statistical effect of average hours spent
by the employees surfing the web on the productivity measured in amount of sales per week (in thousands of dollars). You were given
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 Spring '08
 Petry
 Linear Regression, Regression Analysis

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