$course$/R-exams/Exercise 1 R1 Q1 : swisscapital

What is the seat of the federal authorities in Switzerland (i.e., the de facto capital)?

]]>

There is no de jure capital but the de facto capital and seat of the federal authorities is Bern.

  1. False.
  2. False.
  3. False.
  4. True.
  5. False.

]]> 0 1 false true abc Geneva

]]> False.

]]> St. Gallen

]]> False.

]]> Lausanne

]]> False.

]]> Bern

]]> True.

]]> Basel

]]> False.

]]> R2 Q1 : swisscapital

What is the seat of the federal authorities in Switzerland (i.e., the de facto capital)?

]]>

There is no de jure capital but the de facto capital and seat of the federal authorities is Bern.

  1. False.
  2. False.
  3. False.
  4. True.
  5. False.

]]> 0 1 false true abc Basel

]]> False.

]]> St. Gallen

]]> False.

]]> Vaduz

]]> False.

]]> Bern

]]> True.

]]> Lausanne

]]> False.

]]> R3 Q1 : swisscapital

What is the seat of the federal authorities in Switzerland (i.e., the de facto capital)?

]]>

There is no de jure capital but the de facto capital and seat of the federal authorities is Bern.

  1. False.
  2. True.
  3. False.
  4. False.
  5. False.

]]> 0 1 false true abc Lausanne

]]> False.

]]> Bern

]]> True.

]]> Geneva

]]> False.

]]> St. Gallen

]]> False.

]]> Basel

]]> False.

]]> $course$/R-exams/Exercise 2 R1 Q2 : deriv

What is the derivative of f(x) = x^{3} e^{3.6x}, evaluated at x = 0.72?

]]>

Using the product rule for f(x) = g(x) \cdot h(x), where g(x) := x^{3} and h(x) := e^{3.6x}, we obtain

\begin{aligned} f'(x) & = & [g(x) \cdot h(x)]' = g'(x) \cdot h(x) + g(x) \cdot h'(x) \\ & = & 3 x^{3 - 1} \cdot e^{3.6x} + x^{3} \cdot e^{3.6x} \cdot 3.6 \\ & = & e^{3.6x} \cdot(3 x^2 + 3.6 x^{3}) \\ & = & e^{3.6x} \cdot x^2 \cdot (3 + 3.6x).\end{aligned}

Evaluated at x = 0.72, the answer is

e^{3.6\cdot 0.72} \cdot 0.72^2 \cdot (3 + 3.6\cdot 0.72) = 38.718939.

Thus, rounded to two digits we have f'(0.72) = 38.72.

]]> 0 1 38.72 0.01 R2 Q2 : deriv

What is the derivative of f(x) = x^{5} e^{2.6x}, evaluated at x = 0.53?

]]>

Using the product rule for f(x) = g(x) \cdot h(x), where g(x) := x^{5} and h(x) := e^{2.6x}, we obtain

\begin{aligned} f'(x) & = & [g(x) \cdot h(x)]' = g'(x) \cdot h(x) + g(x) \cdot h'(x) \\ & = & 5 x^{5 - 1} \cdot e^{2.6x} + x^{5} \cdot e^{2.6x} \cdot 2.6 \\ & = & e^{2.6x} \cdot(5 x^4 + 2.6 x^{5}) \\ & = & e^{2.6x} \cdot x^4 \cdot (5 + 2.6x).\end{aligned}

Evaluated at x = 0.53, the answer is

e^{2.6\cdot 0.53} \cdot 0.53^4 \cdot (5 + 2.6\cdot 0.53) = 1.996392.

Thus, rounded to two digits we have f'(0.53) = 2.00.

]]> 0 1 2 0.01 R3 Q2 : deriv

What is the derivative of f(x) = x^{7} e^{2x}, evaluated at x = 0.64?

]]>

Using the product rule for f(x) = g(x) \cdot h(x), where g(x) := x^{7} and h(x) := e^{2x}, we obtain

\begin{aligned} f'(x) & = & [g(x) \cdot h(x)]' = g'(x) \cdot h(x) + g(x) \cdot h'(x) \\ & = & 7 x^{7 - 1} \cdot e^{2x} + x^{7} \cdot e^{2x} \cdot 2 \\ & = & e^{2x} \cdot(7 x^6 + 2 x^{7}) \\ & = & e^{2x} \cdot x^6 \cdot (7 + 2x).\end{aligned}

Evaluated at x = 0.64, the answer is

e^{2\cdot 0.64} \cdot 0.64^6 \cdot (7 + 2\cdot 0.64) = 2.046478.

Thus, rounded to two digits we have f'(0.64) = 2.05.

]]> 0 1 2.05 0.01 $course$/R-exams/Exercise 3 R1 Q3 : ttest

The waiting time (in minutes) at the cashier of two supermarket chains with different cashier systems is compared. The following statistical test was performed:

    Two Sample t-test

data:  Waiting by Supermarket
t = -2.0525, df = 120, p-value = 0.02115
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
       -Inf -0.2212139
sample estimates:
 mean in group Sparag mean in group Consumo 
             4.331325              5.481321

Which of the following statements are correct? (Significance level 5\%)

]]>
  1. True. The absolute value of the test statistic is equal to 2.052.
  2. True. The test aims at showing that the difference of means is smaller than 0.
  3. False. The p value is equal to 0.0211.
  4. False. The test aims at showing that the alternative that the waiting time is shorter at Sparag than at Consumo.
  5. True. The test result is significant (p < 0.05) and hence the alternative is shown, that the difference of means are smaller than 0.

]]> 0 1 false false abc The absolute value of the test statistic is larger than 1.96.

]]> True. The absolute value of the test statistic is equal to 2.052.

]]> A one-sided alternative was tested.

]]> True. The test aims at showing that the difference of means is smaller than 0.

]]> The p value is larger than 0.05.

]]> False. The p value is equal to 0.0211.

]]> The test shows that the waiting time is longer at Sparag than at Consumo.

]]> False. The test aims at showing that the alternative that the waiting time is shorter at Sparag than at Consumo.

]]> The test shows that the waiting time is shorter at Sparag than at Consumo.

]]> True. The test result is significant (p < 0.05) and hence the alternative is shown, that the difference of means are smaller than 0.

]]> R2 Q3 : ttest

The waiting time (in minutes) at the cashier of two supermarket chains with different cashier systems is compared. The following statistical test was performed:

    Two Sample t-test

data:  Waiting by Supermarket
t = -1.9156, df = 117, p-value = 0.05786
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -2.74815480  0.04574051
sample estimates:
 mean in group Sparag mean in group Consumo 
             5.925846              7.277053

Which of the following statements are correct? (Significance level 5\%)

]]>
  1. False. The absolute value of the test statistic is equal to 1.916.
  2. False. The test aims at showing that the difference of means is unequal to 0.
  3. True. The p value is equal to 0.0579.
  4. False. The test result is not significant (p \ge 0.05).
  5. False. The test result ist not significant (p \ge 0.05).

]]> 0 1 false false abc The absolute value of the test statistic is larger than 1.96.

]]> False. The absolute value of the test statistic is equal to 1.916.

]]> A one-sided alternative was tested.

]]> False. The test aims at showing that the difference of means is unequal to 0.

]]> The p value is larger than 0.05.

]]> True. The p value is equal to 0.0579.

]]> The test shows that the waiting time is longer at Sparag than at Consumo.

]]> False. The test result is not significant (p \ge 0.05).

]]> The test shows that the waiting time is shorter at Sparag than at Consumo.

]]> False. The test result ist not significant (p \ge 0.05).

]]> R3 Q3 : ttest

The waiting time (in minutes) at the cashier of two supermarket chains with different cashier systems is compared. The following statistical test was performed:

    Two Sample t-test

data:  Waiting by Supermarket
t = 1.336, df = 135, p-value = 0.0919
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 -0.2010577        Inf
sample estimates:
 mean in group Sparag mean in group Consumo 
             7.067593              6.228852

Which of the following statements are correct? (Significance level 5\%)

]]>
  1. False. The absolute value of the test statistic is equal to 1.336.
  2. True. The test aims at showing that the difference of means is larger than 0.
  3. True. The p value is equal to 0.0919.
  4. False. The test result is not significant (p \ge 0.05).
  5. False. The test aims at showing that the waiting time at Sparag is longer than at Consumo. The test result ist not significant (p \ge 0.05).

]]> 0 1 false false abc The absolute value of the test statistic is larger than 1.96.

]]> False. The absolute value of the test statistic is equal to 1.336.

]]> A one-sided alternative was tested.

]]> True. The test aims at showing that the difference of means is larger than 0.

]]> The p value is larger than 0.05.

]]> True. The p value is equal to 0.0919.

]]> The test shows that the waiting time is longer at Sparag than at Consumo.

]]> False. The test result is not significant (p \ge 0.05).

]]> The test shows that the waiting time is shorter at Sparag than at Consumo.

]]> False. The test aims at showing that the waiting time at Sparag is longer than at Consumo. The test result ist not significant (p \ge 0.05).

]]> $course$/R-exams/Exercise 4 R1 Q4 : boxplots

In the following figure the distributions of a variable given by two samples (A and B) are represented by parallel boxplots. Which of the following statements are correct? (Comment: The statements are either about correct or clearly wrong.)

image

]]> 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
  1. False. Distribution A has on average higher values than distribution B.
  2. True. Both distributions have no observations which deviate more than 1.5 times the interquartile range from the box.
  3. False. The interquartile range in sample A is
    emphnot clearly bigger than in B.
  4. True. The skewness of both distributions is similar, both are about symmetric.
  5. True. Distribution A is about symmetric.

]]> 0 1 false false abc The location of both distributions is about the same.

]]> False. Distribution A has on average higher values than distribution B.

]]> Both distributions contain no outliers.

]]> True. Both distributions have no observations which deviate more than 1.5 times the interquartile range from the box.

]]> The spread in sample A is clearly bigger than in B.

]]> False. The interquartile range in sample A is
emphnot clearly bigger than in B.

]]> The skewness of both samples is similar.

]]> True. The skewness of both distributions is similar, both are about symmetric.

]]> Distribution A is about symmetric.

]]> True. Distribution A is about symmetric.

]]> R2 Q4 : boxplots

In the following figure the distributions of a variable given by two samples (A and B) are represented by parallel boxplots. Which of the following statements are correct? (Comment: The statements are either about correct or clearly wrong.)

image

]]> 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
  1. False. Distribution B has on average higher values than distribution A.
  2. True. Both distributions have no observations which deviate more than 1.5 times the interquartile range from the box.
  3. True. The interquartile range in sample A is clearly bigger than in B.
  4. True. The skewness of both distributions is similar, both are about symmetric.
  5. False. Distribution B is about symmetric.

]]> 0 1 false false abc The location of both distributions is about the same.

]]> False. Distribution B has on average higher values than distribution A.

]]> Both distributions contain no outliers.

]]> True. Both distributions have no observations which deviate more than 1.5 times the interquartile range from the box.

]]> The spread in sample A is clearly bigger than in B.

]]> True. The interquartile range in sample A is clearly bigger than in B.

]]> The skewness of both samples is similar.

]]> True. The skewness of both distributions is similar, both are about symmetric.

]]> Distribution B is left-skewed.

]]> False. Distribution B is about symmetric.

]]> R3 Q4 : boxplots

In the following figure the distributions of a variable given by two samples (A and B) are represented by parallel boxplots. Which of the following statements are correct? (Comment: The statements are either about correct or clearly wrong.)

image

]]> 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
  1. False. Distribution A has on average higher values than distribution B.
  2. True. Both distributions have no observations which deviate more than 1.5 times the interquartile range from the box.
  3. False. The interquartile range in sample A is
    emphnot clearly bigger than in B.
  4. True. The skewness of both distributions is similar, both are about symmetric.
  5. True. Distribution B is about symmetric.

]]> 0 1 false false abc The location of both distributions is about the same.

]]> False. Distribution A has on average higher values than distribution B.

]]> Both distributions contain no outliers.

]]> True. Both distributions have no observations which deviate more than 1.5 times the interquartile range from the box.

]]> The spread in sample A is clearly bigger than in B.

]]> False. The interquartile range in sample A is
emphnot clearly bigger than in B.

]]> The skewness of both samples is similar.

]]> True. The skewness of both distributions is similar, both are about symmetric.

]]> Distribution B is about symmetric.

]]> True. Distribution B is about symmetric.

]]> $course$/R-exams/Exercise 5 R1 Q5 : function

What is the name of the R function for least-squares regression?

]]>

lm is the R function for least-squares regression. See ?lm for the corresponding manual page.

]]> 0 1 0 lm R2 Q5 : function

What is the name of the R function for extracting the estimated covariance matrix from a fitted (generalized) linear model object?

]]>

vcov is the R function for extracting the estimated covariance matrix from a fitted (generalized) linear model object. See ?vcov for the corresponding manual page.

]]> 0 1 0 vcov R3 Q5 : function

What is the name of the R function for Poisson regression?

]]>

glm is the R function for Poisson regression. See ?glm for the corresponding manual page.

]]> 0 1 0 glm $course$/R-exams/Exercise 6 R1 Q6 : lm

Using the data provided in regression.csv estimate a linear regression of y on x and answer the following questions.

  1. {1:MULTICHOICE:%0%x and y are not significantly correlated~%0%y increases significantly with x~%100%y decreases significantly with x}
  2. Estimated slope with respect to x: {1:NUMERICAL:=-0.861:0.01}

]]> 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

image

To replicate the analysis in R:

## data
d <- read.csv("regression.csv")
## regression
m <- lm(y ~ x, data = d)
summary(m)
## visualization
plot(y ~ x, data = d)
abline(m)

]]> 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 0 2 R2 Q6 : lm

Using the data provided in regression.csv estimate a linear regression of y on x and answer the following questions.

  1. {1:MULTICHOICE:%0%x and y are not significantly correlated~%100%y increases significantly with x~%0%y decreases significantly with x}
  2. Estimated slope with respect to x: {1:NUMERICAL:=0.531:0.01}

]]> 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

image

To replicate the analysis in R:

## data
d <- read.csv("regression.csv")
## regression
m <- lm(y ~ x, data = d)
summary(m)
## visualization
plot(y ~ x, data = d)
abline(m)

]]> 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 0 2 R3 Q6 : lm

Using the data provided in regression.csv estimate a linear regression of y on x and answer the following questions.

  1. {1:MULTICHOICE:%100%x and y are not significantly correlated~%0%y increases significantly with x~%0%y decreases significantly with x}
  2. Estimated slope with respect to x: {1:NUMERICAL:=0.024:0.01}

]]> 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

image

To replicate the analysis in R:

## data
d <- read.csv("regression.csv")
## regression
m <- lm(y ~ x, data = d)
summary(m)
## visualization
plot(y ~ x, data = d)
abline(m)

]]> 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 0 2 $course$/R-exams/Exercise 7 R1 Q7 : fourfold2

An industry-leading company seeks a qualified candidate for a management position. A management consultancy carries out an assessment center which concludes in making a positive or negative recommendation for each candidate: From previous assessments they know that of those candidates that are actually eligible for the position (event E) 74\% get a positive recommendation (event R). However, out of those candidates that are not eligible 79\% get a negative recommendation. Overall, they know that only 6\% of all job applicants are actually eligible.

What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)

 R   \overline{R}  sum
 E    {1:NUMERICAL:=4.44:0.05~%0%689609:0}%    {1:NUMERICAL:=1.56:0.05~%0%689609:0}%    {1:NUMERICAL:=6:0.05~%0%689609:0}% 
 \overline{E}    {1:NUMERICAL:=19.74:0.05~%0%689609:0}%    {1:NUMERICAL:=74.26:0.05~%0%689609:0}%    {1:NUMERICAL:=94:0.05~%0%689609:0}% 
sum   {1:NUMERICAL:=24.18:0.05~%0%689609:0}%    {1:NUMERICAL:=75.82:0.05~%0%689609:0}%    {1:NUMERICAL:=100:0.05~%0%689609:0}% 

]]>

Using the information from the text, we can directly calculate the following joint probabilities:

\begin{aligned} P(E \cap R) & = & P(R | E) \cdot P(E) = 0.74 \cdot 0.06 = 0.0444 = 4.44\%\\ P(\overline{E} \cap \overline{R}) & = & P(\overline{R} | \overline{E}) \cdot P(\overline{E}) = 0.79 \cdot 0.94 = 0.7426 = 74.26\%.\end{aligned}

The remaining probabilities can then be found by calculating sums and differences in the fourfold table:

 R   \overline{R}  sum
 E   4.44   1.56   6.00 
 \overline{E}   19.74   74.26   94.00 
sum  24.18   75.82   100.00 
  1. P(E \cap R) = 4.44\%
  2. P(\overline{E} \cap R) = 19.74\%
  3. P(E \cap \overline{R}) = 1.56\%
  4. P(\overline{E} \cap \overline{R}) = 74.26\%
  5. P(R) = 24.18\%
  6. P(\overline{R}) = 75.82\%
  7. P(E) = 6.00\%
  8. P(\overline{E}) = 94.00\%
  9. P(\Omega) = 100.00\%

]]> 0 9 R2 Q7 : fourfold2

An industry-leading company seeks a qualified candidate for a management position. A management consultancy carries out an assessment center which concludes in making a positive or negative recommendation for each candidate: From previous assessments they know that of those candidates that are actually eligible for the position (event E) 72\% get a positive recommendation (event R). However, out of those candidates that are not eligible 74\% get a negative recommendation. Overall, they know that only 8\% of all job applicants are actually eligible.

What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)

 R   \overline{R}  sum
 E    {1:NUMERICAL:=5.76:0.05~%0%216905:0}%    {1:NUMERICAL:=2.24:0.05~%0%216905:0}%    {1:NUMERICAL:=8:0.05~%0%216905:0}% 
 \overline{E}    {1:NUMERICAL:=23.92:0.05~%0%216905:0}%    {1:NUMERICAL:=68.08:0.05~%0%216905:0}%    {1:NUMERICAL:=92:0.05~%0%216905:0}% 
sum   {1:NUMERICAL:=29.68:0.05~%0%216905:0}%    {1:NUMERICAL:=70.32:0.05~%0%216905:0}%    {1:NUMERICAL:=100:0.05~%0%216905:0}% 

]]>

Using the information from the text, we can directly calculate the following joint probabilities:

\begin{aligned} P(E \cap R) & = & P(R | E) \cdot P(E) = 0.72 \cdot 0.08 = 0.0576 = 5.76\%\\ P(\overline{E} \cap \overline{R}) & = & P(\overline{R} | \overline{E}) \cdot P(\overline{E}) = 0.74 \cdot 0.92 = 0.6808 = 68.08\%.\end{aligned}

The remaining probabilities can then be found by calculating sums and differences in the fourfold table:

 R   \overline{R}  sum
 E   5.76   2.24   8.00 
 \overline{E}   23.92   68.08   92.00 
sum  29.68   70.32   100.00 
  1. P(E \cap R) = 5.76\%
  2. P(\overline{E} \cap R) = 23.92\%
  3. P(E \cap \overline{R}) = 2.24\%
  4. P(\overline{E} \cap \overline{R}) = 68.08\%
  5. P(R) = 29.68\%
  6. P(\overline{R}) = 70.32\%
  7. P(E) = 8.00\%
  8. P(\overline{E}) = 92.00\%
  9. P(\Omega) = 100.00\%

]]> 0 9 R3 Q7 : fourfold2

An industry-leading company seeks a qualified candidate for a management position. A management consultancy carries out an assessment center which concludes in making a positive or negative recommendation for each candidate: From previous assessments they know that of those candidates that are actually eligible for the position (event E) 65\% get a positive recommendation (event R). However, out of those candidates that are not eligible 75\% get a negative recommendation. Overall, they know that only 10\% of all job applicants are actually eligible.

What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)

 R   \overline{R}  sum
 E    {1:NUMERICAL:=6.5:0.05~%0%124381:0}%    {1:NUMERICAL:=3.5:0.05~%0%124381:0}%    {1:NUMERICAL:=10:0.05~%0%124381:0}% 
 \overline{E}    {1:NUMERICAL:=22.5:0.05~%0%124381:0}%    {1:NUMERICAL:=67.5:0.05~%0%124381:0}%    {1:NUMERICAL:=90:0.05~%0%124381:0}% 
sum   {1:NUMERICAL:=29:0.05~%0%124381:0}%    {1:NUMERICAL:=71:0.05~%0%124381:0}%    {1:NUMERICAL:=100:0.05~%0%124381:0}% 

]]>

Using the information from the text, we can directly calculate the following joint probabilities:

\begin{aligned} P(E \cap R) & = & P(R | E) \cdot P(E) = 0.65 \cdot 0.1 = 0.065 = 6.5\%\\ P(\overline{E} \cap \overline{R}) & = & P(\overline{R} | \overline{E}) \cdot P(\overline{E}) = 0.75 \cdot 0.9 = 0.675 = 67.5\%.\end{aligned}

The remaining probabilities can then be found by calculating sums and differences in the fourfold table:

 R   \overline{R}  sum
 E   6.50   3.50   10.00 
 \overline{E}   22.50   67.50   90.00 
sum  29.00   71.00   100.00 
  1. P(E \cap R) = 6.5\%
  2. P(\overline{E} \cap R) = 22.5\%
  3. P(E \cap \overline{R}) = 3.5\%
  4. P(\overline{E} \cap \overline{R}) = 67.5\%
  5. P(R) = 29.0\%
  6. P(\overline{R}) = 71.0\%
  7. P(E) = 10.0\%
  8. P(\overline{E}) = 90.0\%
  9. P(\Omega) = 100.0\%

]]> 0 9