Eurovision Song Contest 2021 Statistics Analysis

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Questions and Answers

What is the purpose of using bookmakers' scores as an instrument in the regression analysis?

To predict the final rank of the contestants accurately

To measure the impact of public scores on the jury's decisions

To reduce measurement errors in the public scores (correct)

To examine the relationship between moment of performance and public scores

What does the negative coefficient for 'Winning probability' in the TSLS results suggest?

Higher winning probability leads to higher public scores

Higher winning probability has no effect on public scores

The winning probability is not statistically significant

Higher winning probability leads to lower public scores (correct)

Why is it mentioned that bookmakers' scores should be exogenous in the context presented?

To highlight their independence from the public votes (correct)

To stress their direct relation to the final rank

To point out their reliance on historical data

To emphasize their correlation with the jury's opinions

What does the OLS estimator biasing towards zero suggest about the measurement errors?

Measurement errors lead to an underestimation of the true relationship Signup and view all the answers

What do 95% confidence intervals for 𝛽 including the value of 1 imply?

The OLS estimator is unbiased Signup and view all the answers

What does the test for exogeneity of public scores suggest with p values of 0.000 and 0.003 for the two instruments?

Public scores are endogenous in the regression analysis Signup and view all the answers

What does the scatter plot in Figure 5.1 suggest about the correlation between score given by the professional jury and the public?

There is a strong positive correlation Signup and view all the answers

What does it mean if the regression line for the data in the scatter plot has a slope equal to 1?

There is a perfect positive correlation Signup and view all the answers

What is the estimated value of β in the OLS model 𝑐𝑜𝑟𝑒 𝑗𝑢𝑟𝑦𝑖 = 𝛼 +𝛽 𝑆𝑐𝑜𝑟𝑒 𝑝𝑢𝑏𝑙𝑖𝑐𝑖 +𝜀𝑖?

0.526 Signup and view all the answers

What does it mean if the value 1 is not included in the 95% confidence interval for β?

There is a significant difference between how the professional jury and public rate contestants Signup and view all the answers

What could be a reason for the public's scores possibly suffering from measurement error according to Table 5.1?

Experiencing order effects due to how performances were presented Signup and view all the answers

Based on the OLS model results, what can be inferred about the relationship between score jury and score public?

The relationship is perfectly linear Signup and view all the answers

Study Notes

Eurovision Song Contest Statistics

The table provides statistics on the Eurovision Song Contest 2021, including the rank, moment of performance, score, jury score, and public score.
The scatter plot of the score jury versus score public suggests a strong correlation, with a correlation coefficient of 0.618.

Regression Analysis

The OLS regression model is: score_jury = α + β score_public + ε
The regression result is: α = 41.254 and β = 0.526 with R² = 0.382
The 95% confidence interval for β ranges from 0.254 to 0.798, excluding the value 1.

Order Effects

The public scores may suffer from measurement error due to order effects, where the public remembers more from recent performances than from earlier ones.
The moment of performance is not related to the score of the jury.
However, the moment of performance has a positive effect on the scores given by the public.

Instrumental Variable Approach

The scores given by bookmakers are used as an instrument for the scores of the public.
The bookmakers' winning probabilities and rank are presented in Table 5.2.
The instrumental variable approach using the bookmakers' winning probabilities yields: α = -48.477 and β = 1.557
The instrumental variable approach using the bookmakers' rank yields: α = -5.018 and β = 1.058
The 95% confidence intervals for β include the value of 1, confirming that the measurement errors bias the OLS estimator for β towards zero.

Test for Exogeneity

The test for the null hypothesis of exogeneity of the scores of the public yields: 18.466 (p value 0.000) and 8.708 (p value 0.003) respectively, confirming that the scores of the public are not exogenous.

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Description

Explore the statistics of the Eurovision Song Contest 2021 and analyze the rankings, moments of performance, jury scores, and public scores of the contestants. Determine if there is a correlation between the professional jury's scores and the public's ratings.