University of Cape Town – Department of Statistical Sciences
STA2020S Exam November 2022
Examiners: Mr. Ehsaan Rajak Marks: 100
Mr. Neil Watson Internal Examiner: Mr. Stefan Britz
External examiner: Prof G.D Sharp
Instructions:
• You have 3 hours to complete this exam
• Answer ALL questions
• Marks are awarded for intermediate calculations
• Round all answers to 2 decimal places unless otherwise specified. Round intermediary calculations to
three decimal places.
• Answer Section A on the MCQ sheet provided; Sections B and C in one answer book and Section D and
Section E in one answer book. You should hand in 2 answer books in total.
• Start section C on a NEW page in your first answer book, and start section E on a new page in your
second answer book
• For all MCQ questions, select the MOST correct answer
Section A: MCQ [30]
Question 1 (2)
Consider a Completely Randomised Block Design experiment with 3 treatments and 5 levels of the blocking
variable. We summarise some of data obtained from this experiment in the table below.
BLOCK 1 BLOCK 2 BLOCK 3 BLOCK 4 BLOCK 5
MEANS 18 7 X3 6 X 14 x 3 10
x3 3 3
54 21 18 42 3
What is the Block SS if you were to conduct a Randomised Complete Block Design ANOVA to test for difference
in means?
A) 300
16532
Sf 3
B) 33.33 21 t 4327305
C) 546 183
D) 60.67 IS
E) None of the above
300
Question 2 (2)
Which one of the following statements is FALSE?
A) ANOVA assumes samples are obtained from approximately normally distributed populations
B) An assumption of ANOVA is that the samples are independent
C) Two-Way ANOVA is useful because it can provide information on how variables interact
D) A relatively small F-stat indicates a significant factor
small p large 2 significant
or
E) None of the above statements are false
Page 1
, Question 3 (2)
The degrees of freedom for the interaction term in a Two Way ANOVA with 4 levels for the first factor and 5
levels for the second is…
A) 12
B) 20 Ca 1 1 b
C) 4
D) 5 4 1 S 1
E) 1
12
Question 4 f stat but no sig t stat (2)
dsig
Multicollinearity …
A) is always present in a simple linear regression model
X
B) is only considered if the adjusted R-squared value is low
OC)D) Can lead to unstable estimates
Exists when the residuals are large
E) Exists when there is high correlation between the independent and a dependent variable.
x
Question 5 (2)
Stepwise procedures always produce the best possible model, because they depend on AIC
A) This statement is false, because the model could contain redundant predictors which would negatively
affect stepwise procedures.
B) This statement is true, because stepwise procedures are iterative and only add/remove a variable if it
improves the model and AIC is a good measure of the quality of a model
C) This statement is true, because stepwise procedures eliminate human error.
D) This statement is true, because AIC balances goodness of fit and complexity
E) The statement is false, because there are better measurements to assess the quality of a model (for
example adjusted R-squared)
Priti
Question 6 dean'thappen odds In(2) f
Logistic regression is used when … ingens odds inFp
A)
B)
The dependent variable is binary
slog
The dependent variable is continuous, and the independent variables are binary
C)
D)
There is a combination of binary and continuous explanatory variables
The independent variable is binary
Iecporpix
potpie
E) A multiple regression model is not working for a continuous response variable e
BorBix
Question 7 ArYigfferenced (2)
When is an ARIMA(1,1,0) model appropriate for a time series?
A) When the ACF decays to 0 slowly and the PACF does not decay to 0
B) When the PACF decays to 0 slowly and the ACF does not decay to 0
C) When the PACF decays to 0 quickly and the ACF cuts off sharply after one non-zero spike
D) When the ACF decays to 0 quickly and the PACF cuts off sharply after one non-zero spike
E) When the ACF decays to 0 slowly and the PACF cuts off sharply after one non-zero spike
Page 2
Hii HII
decay cuts
Aries
STA2020S Exam November 2022
Examiners: Mr. Ehsaan Rajak Marks: 100
Mr. Neil Watson Internal Examiner: Mr. Stefan Britz
External examiner: Prof G.D Sharp
Instructions:
• You have 3 hours to complete this exam
• Answer ALL questions
• Marks are awarded for intermediate calculations
• Round all answers to 2 decimal places unless otherwise specified. Round intermediary calculations to
three decimal places.
• Answer Section A on the MCQ sheet provided; Sections B and C in one answer book and Section D and
Section E in one answer book. You should hand in 2 answer books in total.
• Start section C on a NEW page in your first answer book, and start section E on a new page in your
second answer book
• For all MCQ questions, select the MOST correct answer
Section A: MCQ [30]
Question 1 (2)
Consider a Completely Randomised Block Design experiment with 3 treatments and 5 levels of the blocking
variable. We summarise some of data obtained from this experiment in the table below.
BLOCK 1 BLOCK 2 BLOCK 3 BLOCK 4 BLOCK 5
MEANS 18 7 X3 6 X 14 x 3 10
x3 3 3
54 21 18 42 3
What is the Block SS if you were to conduct a Randomised Complete Block Design ANOVA to test for difference
in means?
A) 300
16532
Sf 3
B) 33.33 21 t 4327305
C) 546 183
D) 60.67 IS
E) None of the above
300
Question 2 (2)
Which one of the following statements is FALSE?
A) ANOVA assumes samples are obtained from approximately normally distributed populations
B) An assumption of ANOVA is that the samples are independent
C) Two-Way ANOVA is useful because it can provide information on how variables interact
D) A relatively small F-stat indicates a significant factor
small p large 2 significant
or
E) None of the above statements are false
Page 1
, Question 3 (2)
The degrees of freedom for the interaction term in a Two Way ANOVA with 4 levels for the first factor and 5
levels for the second is…
A) 12
B) 20 Ca 1 1 b
C) 4
D) 5 4 1 S 1
E) 1
12
Question 4 f stat but no sig t stat (2)
dsig
Multicollinearity …
A) is always present in a simple linear regression model
X
B) is only considered if the adjusted R-squared value is low
OC)D) Can lead to unstable estimates
Exists when the residuals are large
E) Exists when there is high correlation between the independent and a dependent variable.
x
Question 5 (2)
Stepwise procedures always produce the best possible model, because they depend on AIC
A) This statement is false, because the model could contain redundant predictors which would negatively
affect stepwise procedures.
B) This statement is true, because stepwise procedures are iterative and only add/remove a variable if it
improves the model and AIC is a good measure of the quality of a model
C) This statement is true, because stepwise procedures eliminate human error.
D) This statement is true, because AIC balances goodness of fit and complexity
E) The statement is false, because there are better measurements to assess the quality of a model (for
example adjusted R-squared)
Priti
Question 6 dean'thappen odds In(2) f
Logistic regression is used when … ingens odds inFp
A)
B)
The dependent variable is binary
slog
The dependent variable is continuous, and the independent variables are binary
C)
D)
There is a combination of binary and continuous explanatory variables
The independent variable is binary
Iecporpix
potpie
E) A multiple regression model is not working for a continuous response variable e
BorBix
Question 7 ArYigfferenced (2)
When is an ARIMA(1,1,0) model appropriate for a time series?
A) When the ACF decays to 0 slowly and the PACF does not decay to 0
B) When the PACF decays to 0 slowly and the ACF does not decay to 0
C) When the PACF decays to 0 quickly and the ACF cuts off sharply after one non-zero spike
D) When the ACF decays to 0 quickly and the PACF cuts off sharply after one non-zero spike
E) When the ACF decays to 0 slowly and the PACF cuts off sharply after one non-zero spike
Page 2
Hii HII
decay cuts
Aries
