Math104 – Fall ‘14

Math 104 – Fall ‘14
Applied Regression Analysis
Lab Assignment #8: Model Building
Due: November 17, 2014

Name

ID#

Department of Mathematics
GOLDEN GATE UNIVERSITY

[1] A research analyst for an oil company
wants to develop a model to predict miles per gallon based on highway
speed. An experiment is designed in
which a test car is driven at speeds ranging from 10 miles per hour to 75 miles
per hour. The results are in the data set
(SPEED.xls).
a)
Set
up a scatter diagram for speed and miles per gallon.
b)
Apply
simple regression analysis, and then interpret the meaning of the slope b1 in this problem.
c)
Interpret
the meaning of the regression coefficientb0 in this problem.
d)
Determine
the coefficient of determination,r2, and interpret its meaning.
e)
How
useful do you think this regression model is for predicting mileage?

[2] Refer to the data set given in [1]. Now assume a quadratic relationship between
speed and mileage:
a)
State
the quadratic regression equation.
b)
Predict
the average mileage obtained when the car is driven at 55 miles per hour.
c)
Determine
the coefficient of multiple determination,r2.
d)
Determine
the adjustedr2.
e)
Determine
the adequacy of the fit of the model.
f)
At
the 0.05 level of significance, determine whether the quadratic model is a
better fit than the linear regression model.

[3] An auto manufacturing company wanted to
investigate how the price of one of its car models depreciates with age. The research department at the company took a
sample of eight cars of this model and collected the following information on
the ages (in years) and prices (in hundreds of dollars) of these cars. The data are in USEDCAR.xls.

Age (x)

8

3

6

9

2

5

6

3

Price (y)

16

74

40

19

124

36

33

89

a)
Set
up a scatter diagram for age and price.
b)
At
the 0.05 level of significance, determine whether there is a significant linear
relationship between age and price.
c)
State
the linear regression equation.
d)
Predict
the average price obtained when the age of the car is 7 years old.
e)
Determine
the coefficient of determination,r2, and interpret its meaning.
f)
How
useful do you think this regression model is for predicting price?

[4] Refer to the data set given in [3]. Now assume a quadratic relationship between age
and price:
a)
State
the quadratic regression equation.
b)
Predict
the average price obtained when the age of the car is 7 years old.
c)
Determine
the coefficient of multiple determination,r2.
d)
Determine
the adjustedr2.
e)
Determine
the adequacy of the fit of the model.
f)
At
the 0.05 level of significance, determine whether the quadratic model is a
better fit than the linear regression model.

[5]
Refer to the data set given in [3].
Perform a natural or common logarithmic transformation of the dependent
variable (price).
a)
State
the regression equation.
b)
Predict
the average price obtained when the age of the car is 7 years old.
c)
Determine
the coefficient of multiple determination,r2.
d)
Determine
the adjustedr2.
e)
Determine
the adequacy of the fit of the model.
f)
Compare
your results in [3], [4], and [5]. Which
model is best? Why?