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Quantitative Methods for Business & Management
Frank Dewhurst, UMIST, UK
Modelling simple relationships
Self-test Questions
1
When drawing a scattergram, the independent variable should be put on the
A)
data points
B)
vertical axis
C)
origin
D)
line
E)
horizontal axis
2
In the expression x = f(y), the ‘f’ stands for
A)
function
B)
factor
C)
filter
D)
frequency
E)
factorial
3
In the expression
(1.0K)
which is the dependant variable?
A)
y
B)
(0.0K)
C)
(0.0K)
D)
z
E)
f
4
If b is negative in the linear equation y = ax + b, then the line on the graph is
A)
Downwards from left to right
B)
Flat
C)
Upwards from left to right
D)
Flat or up or down from left to right
E)
Curved
5
What is least squares linear regression?
A)
A technique for comparing the means of two data sets
B)
A technique for drawing scattergrams
C)
A technique for comparing the probability distributions of two datasets
D)
A technique for calculating the correlation coefficient for paired observations
E)
A technique for establishing the straight line of best fit for paired observations
6
Why is the MAE (mean absolute error) less useful than the MSE (mean squared error) for fitting linear regression lines?
A)
MAE is always bigger than MSE
B)
MAE is always smaller than MSE
C)
Formulae are available for a and b using MSE
D)
MAE is subject to random error
E)
MSE is more accurate
7
The ‘least’ in least squares regression relates to the minimisation of the distance of the regression line from the origin.
A)
TRUE
B)
FALSE
8
The coefficient of determination is the square root of the correlation coefficient.
A)
TRUE
B)
FALSE
9
A value of the coefficient of determination close to 1 or to –1 tells us that
A)
The linear regression is a good fit to the data
B)
The linear regression is a poor fit to the data
C)
The values of x do not vary much
D)
The values of y do not vary much
E)
The relationship probably is not linear
10
Which of the following is not an inappropriate use of a linear model y = ax+b?
A)
Using the model to predict values of y for any values of x
B)
Using the model because it is easy to calculate a and b, even though another type of model fits better
C)
Using the model to predict values of y for values of x close to or within the range of the original dataset
D)
Using the model when there is no theoretical reason for a relationship between x and y
E)
Using the model to prove spurious relationships
11
Another name for the ‘range of applicability’ of a model is the ‘________ of the function’
A)
Determinant
B)
Domain
C)
Inverse
D)
Minimum
12
What is the general form of a linear equation?
A)
y = c
B)
y = ax + b
C)
(1.0K)
D)
y = x + 1
E)
y = (a/x) + b
13
In the linear function y = ax + b, ‘a’ defines the intercept.
A)
TRUE
B)
FALSE
14
A linear function y = ax + b always defines a straight line, regardless of the values of ‘a’ and ‘b’.
A)
TRUE
B)
FALSE
15
If y = ax + b, where a = 4 and b = -2, what is the value of y when x = 2?
A)
2
B)
4
C)
6
D)
8
E)
10
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