Which model would you select? Explain your choice and the criteria used to reach your decision.
Which model would you select? Explain your choice and the criteria used to reach your decision.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![14.53 The article "The Analysis and Selection of
Variables in Linear Regression" (Biometrics [1976]: 1-
49) reports on an analysis of data taken from issues of
Motor Trend magazine. The dependent variable y was gas
mileage; there were n = 32 observations; and the inde-
pendent variables were x₁ = engine type (1 = straight,
0 = V), x₂ = number of cylinders, x3 = transmission
type (1 = manual, 0 = automatic), x4 = number of
transmission speeds, x, = engine size, x6 = horsepower,
x = number of carburetor barrels, xg = final drive ratio,
x9 = weight, and x₁0 = quarter-mile time. The R² and
adjusted R² values are given in the accompanying table
for the best model using k predictors for k = 1, ..., 10.
Which model would you select? Explain your choice and
the criteria used to reach your decision.
X10
k
1
2
3
4
5
6
7
8
9
10
Variables Included
X2, X9
X3, X9, X10
X3, X6 X9, X10
X3, X5, X6, X9, X10
X3, X5, X6 X8, X, X10
X3 X4 X5, X6, X8, X9, X10
X3 X4 X5, X6, X7, X8, X9, X10
X1, X3, X4, X5, X6 X7, X8, X9, X10
All independent
variables
R²
.756
.833
.852
.860
.866
.869
.870
.871
.871
.871
Adjusted R²
.748
.821
.836
.839
.840
.837
.832
.826
.818
.809](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F143fb460-ca06-4a28-85d3-f8c7f8657182%2F01c44c31-8254-42a5-9492-973a3563d27c%2Ffgm9tmm_processed.png&w=3840&q=75)
Transcribed Image Text:14.53 The article "The Analysis and Selection of
Variables in Linear Regression" (Biometrics [1976]: 1-
49) reports on an analysis of data taken from issues of
Motor Trend magazine. The dependent variable y was gas
mileage; there were n = 32 observations; and the inde-
pendent variables were x₁ = engine type (1 = straight,
0 = V), x₂ = number of cylinders, x3 = transmission
type (1 = manual, 0 = automatic), x4 = number of
transmission speeds, x, = engine size, x6 = horsepower,
x = number of carburetor barrels, xg = final drive ratio,
x9 = weight, and x₁0 = quarter-mile time. The R² and
adjusted R² values are given in the accompanying table
for the best model using k predictors for k = 1, ..., 10.
Which model would you select? Explain your choice and
the criteria used to reach your decision.
X10
k
1
2
3
4
5
6
7
8
9
10
Variables Included
X2, X9
X3, X9, X10
X3, X6 X9, X10
X3, X5, X6, X9, X10
X3, X5, X6 X8, X, X10
X3 X4 X5, X6, X8, X9, X10
X3 X4 X5, X6, X7, X8, X9, X10
X1, X3, X4, X5, X6 X7, X8, X9, X10
All independent
variables
R²
.756
.833
.852
.860
.866
.869
.870
.871
.871
.871
Adjusted R²
.748
.821
.836
.839
.840
.837
.832
.826
.818
.809
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