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"markdown": "---\nformat:\n revealjs:\n embed-resources: true\n css: webex.css\n include-after-body: webex.js\n scrollable: true\n---\n\n\n\n\n\n## Numeric\n\n\n\n::: {.webex-group}\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhat is the name of the R function for extracting the estimated covariance matrix from a fitted (generalized) linear model object?\n\n\n\n:::\n::: {.webex-solution}\n\n`vcov` is the R function for extracting the estimated covariance matrix from a fitted (generalized) linear model object.\nSee `?vcov` for the corresponding manual page.\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhat is the name of the R function for extracting the estimated coefficients from a fitted (generalized) linear model object?\n\n\n\n:::\n::: {.webex-solution}\n\n`coef` is the R function for extracting the estimated coefficients from a fitted (generalized) linear model object.\nSee `?coef` for the corresponding manual page.\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhat is the name of the R function for negative binomial regression?\n\n\n\n:::\n::: {.webex-solution}\n\n`glm.nb` is the R function for negative binomial regression.\nSee `?glm.nb` for the corresponding manual page.\n\n:::\n\n:::\n:::\n\n\n\n## Single schoice\n\n\n\n::: {.webex-group}\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhat is the seat of the federal authorities in Switzerland (i.e., the de facto capital)?\n\n\n\n\n\n:::\n::: {.webex-solution}\n\nThere is no de jure capital but the de facto capital and seat of the federal authorities is Bern.\n\n\n* False\n* True\n* False\n* False\n* False\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhat is the seat of the federal authorities in Switzerland (i.e., the de facto capital)?\n\n\n\n\n\n:::\n::: {.webex-solution}\n\nThere is no de jure capital but the de facto capital and seat of the federal authorities is Bern.\n\n\n* False\n* True\n* False\n* False\n* False\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhat is the seat of the federal authorities in Switzerland (i.e., the de facto capital)?\n\n\n\n\n\n:::\n::: {.webex-solution}\n\nThere is no de jure capital but the de facto capital and seat of the federal authorities is Bern.\n\n\n* True\n* False\n* False\n* False\n* False\n\n:::\n\n:::\n:::\n\n\n\n## Multiple choice\n\n\n\n::: {.webex-group}\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhich of the following statements about Switzerland is correct?\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n\n* False. Switzerland is part of the Schengen Area but not the EU.\n* True. The official languages are: German, French, Italian, Romansh.\n* False. There is no de jure capital but the de facto capital of Switzerland is Bern.\n* False. The currency is the Swiss Franc (CHF).\n* True. The establishment of the Swiss Confederation is traditionally dated to August 1, 1291.\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhich of the following statements about Switzerland is correct?\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n\n* False. There is no de jure capital but the de facto capital of Switzerland is Bern.\n* True. The establishment of the Swiss Confederation is traditionally dated to August 1, 1291.\n* False. The currency is the Swiss Franc (CHF).\n* False. Switzerland is part of the Schengen Area but not the EU.\n* True. The official languages are: German, French, Italian, Romansh.\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\nWhich of the following statements about Switzerland is correct?\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n\n* False. The currency is the Swiss Franc (CHF).\n* True. The establishment of the Swiss Confederation is traditionally dated to August 1, 1291.\n* False. Switzerland is part of the Schengen Area but not the EU.\n* True. The official languages are: German, French, Italian, Romansh.\n* False. There is no de jure capital but the de facto capital of Switzerland is Bern.\n\n:::\n\n:::\n:::\n\n\n\n## Cloze\n\n\n\n::: {.webex-group}\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\n\n**Theory:** Consider a linear regression of `y` on `x`. It is usually estimated with\nwhich estimation technique (three-letter abbreviation)?\n\n\n\nThis estimator yields the best linear unbiased estimator (BLUE) under the assumptions\nof the Gauss-Markov theorem. Which of the following properties are required for the\nerrors of the linear regression model under these assumptions?\n\n\n\n\n**Application:** Using the data provided in [linreg.csv](linreg.csv) estimate a\nlinear regression of `y` on `x`. What are the estimated parameters?\n\nIntercept: \n\nSlope: \n\nIn terms of significance at 5% level:\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n**Theory:** Linear regression models are typically estimated by ordinary least squares (OLS).\nThe Gauss-Markov theorem establishes certain optimality properties: Namely, if the errors\nhave expectation zero, constant variance (homoscedastic), no autocorrelation and the\nregressors are exogenous and not linearly dependent, the OLS estimator is the best linear\nunbiased estimator (BLUE).\n\n**Application:** The estimated coefficients along with their significances are reported in the\nsummary of the fitted regression model, showing that `x` and `y` are not significantly correlated (at 5% level).\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\nCall:\nlm(formula = y ~ x, data = d)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.60117 -0.16636 -0.01382 0.17249 0.61989 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|)\n(Intercept) -0.000938 0.025170 -0.037 0.970\nx 0.012960 0.045205 0.287 0.775\n\nResidual standard error: 0.2517 on 98 degrees of freedom\nMultiple R-squared: 0.000838,\tAdjusted R-squared: -0.009358 \nF-statistic: 0.08219 on 1 and 98 DF, p-value: 0.775\n```\n\n\n:::\n:::\n\n**Code:** The analysis can be replicated in R using the following code.\n\n```\n## data\nd <- read.csv(\"linreg.csv\")\n## regression\nm <- lm(y ~ x, data = d)\nsummary(m)\n## visualization\nplot(y ~ x, data = d)\nabline(m)\n```\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\n\n**Theory:** Consider a linear regression of `y` on `x`. It is usually estimated with\nwhich estimation technique (three-letter abbreviation)?\n\n\n\nThis estimator yields the best linear unbiased estimator (BLUE) under the assumptions\nof the Gauss-Markov theorem. Which of the following properties are required for the\nerrors of the linear regression model under these assumptions?\n\n\n\n\n**Application:** Using the data provided in [linreg.csv](linreg.csv) estimate a\nlinear regression of `y` on `x`. What are the estimated parameters?\n\nIntercept: \n\nSlope: \n\nIn terms of significance at 5% level:\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n**Theory:** Linear regression models are typically estimated by ordinary least squares (OLS).\nThe Gauss-Markov theorem establishes certain optimality properties: Namely, if the errors\nhave expectation zero, constant variance (homoscedastic), no autocorrelation and the\nregressors are exogenous and not linearly dependent, the OLS estimator is the best linear\nunbiased estimator (BLUE).\n\n**Application:** The estimated coefficients along with their significances are reported in the\nsummary of the fitted regression model, showing that `x` and `y` are not significantly correlated (at 5% level).\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\nCall:\nlm(formula = y ~ x, data = d)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.55238 -0.13598 -0.00583 0.16578 0.48354 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|)\n(Intercept) 0.02644 0.02338 1.131 0.261\nx 0.04149 0.04378 0.948 0.346\n\nResidual standard error: 0.2337 on 98 degrees of freedom\nMultiple R-squared: 0.009082,\tAdjusted R-squared: -0.00103 \nF-statistic: 0.8982 on 1 and 98 DF, p-value: 0.3456\n```\n\n\n:::\n:::\n\n**Code:** The analysis can be replicated in R using the following code.\n\n```\n## data\nd <- read.csv(\"linreg.csv\")\n## regression\nm <- lm(y ~ x, data = d)\nsummary(m)\n## visualization\nplot(y ~ x, data = d)\nabline(m)\n```\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\n\n**Theory:** Consider a linear regression of `y` on `x`. It is usually estimated with\nwhich estimation technique (three-letter abbreviation)?\n\n\n\nThis estimator yields the best linear unbiased estimator (BLUE) under the assumptions\nof the Gauss-Markov theorem. Which of the following properties are required for the\nerrors of the linear regression model under these assumptions?\n\n\n\n\n**Application:** Using the data provided in [linreg.csv](linreg.csv) estimate a\nlinear regression of `y` on `x`. What are the estimated parameters?\n\nIntercept: \n\nSlope: \n\nIn terms of significance at 5% level:\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n**Theory:** Linear regression models are typically estimated by ordinary least squares (OLS).\nThe Gauss-Markov theorem establishes certain optimality properties: Namely, if the errors\nhave expectation zero, constant variance (homoscedastic), no autocorrelation and the\nregressors are exogenous and not linearly dependent, the OLS estimator is the best linear\nunbiased estimator (BLUE).\n\n**Application:** The estimated coefficients along with their significances are reported in the\nsummary of the fitted regression model, showing that `x` and `y` are not significantly correlated (at 5% level).\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\nCall:\nlm(formula = y ~ x, data = d)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.69939 -0.15033 0.00787 0.19347 0.71812 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|)\n(Intercept) -0.01384 0.02665 -0.519 0.605\nx 0.01161 0.04185 0.277 0.782\n\nResidual standard error: 0.2664 on 98 degrees of freedom\nMultiple R-squared: 0.000784,\tAdjusted R-squared: -0.009412 \nF-statistic: 0.0769 on 1 and 98 DF, p-value: 0.7821\n```\n\n\n:::\n:::\n\n**Code:** The analysis can be replicated in R using the following code.\n\n```\n## data\nd <- read.csv(\"linreg.csv\")\n## regression\nm <- lm(y ~ x, data = d)\nsummary(m)\n## visualization\nplot(y ~ x, data = d)\nabline(m)\n```\n\n:::\n\n:::\n:::\n\n\n\n## Cloze (devel)\n\n\n\n::: {.webex-group}\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\n\n**Theory:** Consider a linear regression of `y` on `x`. It is usually estimated with\nwhich estimation technique (three-letter abbreviation)?\n\n\n\nThis estimator yields the best linear unbiased estimator (BLUE) under the assumptions\nof the Gauss-Markov theorem. Which of the following properties are required for the\nerrors of the linear regression model under these assumptions?\n\n\n\n\n**Application:** Using the data provided in [linreg.csv](linreg.csv) estimate a\nlinear regression of `y` on `x`. What are the estimated parameters?\n\nIntercept: \n\nSlope: \n\nIn terms of significance at 5% level:\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n**Theory:** Linear regression models are typically estimated by ordinary least squares (OLS).\nThe Gauss-Markov theorem establishes certain optimality properties: Namely, if the errors\nhave expectation zero, constant variance (homoscedastic), no autocorrelation and the\nregressors are exogenous and not linearly dependent, the OLS estimator is the best linear\nunbiased estimator (BLUE).\n\n**Application:** The estimated coefficients along with their significances are reported in the\nsummary of the fitted regression model, showing that `y` increases significantly with `x` (at 5% level).\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\nCall:\nlm(formula = y ~ x, data = d)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.64113 -0.19266 -0.00584 0.21850 0.70920 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 0.02206 0.02807 0.786 0.434 \nx 0.70713 0.05027 14.066 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.2806 on 98 degrees of freedom\nMultiple R-squared: 0.6687,\tAdjusted R-squared: 0.6654 \nF-statistic: 197.8 on 1 and 98 DF, p-value: < 2.2e-16\n```\n\n\n:::\n:::\n\n**Code:** The analysis can be replicated in R using the following code.\n\n```\n## data\nd <- read.csv(\"linreg.csv\")\n## regression\nm <- lm(y ~ x, data = d)\nsummary(m)\n## visualization\nplot(y ~ x, data = d)\nabline(m)\n```\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\n\n**Theory:** Consider a linear regression of `y` on `x`. It is usually estimated with\nwhich estimation technique (three-letter abbreviation)?\n\n\n\nThis estimator yields the best linear unbiased estimator (BLUE) under the assumptions\nof the Gauss-Markov theorem. Which of the following properties are required for the\nerrors of the linear regression model under these assumptions?\n\n\n\n\n**Application:** Using the data provided in [linreg.csv](linreg.csv) estimate a\nlinear regression of `y` on `x`. What are the estimated parameters?\n\nIntercept: \n\nSlope: \n\nIn terms of significance at 5% level:\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n**Theory:** Linear regression models are typically estimated by ordinary least squares (OLS).\nThe Gauss-Markov theorem establishes certain optimality properties: Namely, if the errors\nhave expectation zero, constant variance (homoscedastic), no autocorrelation and the\nregressors are exogenous and not linearly dependent, the OLS estimator is the best linear\nunbiased estimator (BLUE).\n\n**Application:** The estimated coefficients along with their significances are reported in the\nsummary of the fitted regression model, showing that `y` increases significantly with `x` (at 5% level).\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\nCall:\nlm(formula = y ~ x, data = d)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.73372 -0.15283 0.01776 0.15444 0.56256 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.02724 0.02554 -1.066 0.289 \nx 0.88110 0.04402 20.016 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.2554 on 98 degrees of freedom\nMultiple R-squared: 0.8035,\tAdjusted R-squared: 0.8015 \nF-statistic: 400.6 on 1 and 98 DF, p-value: < 2.2e-16\n```\n\n\n:::\n:::\n\n**Code:** The analysis can be replicated in R using the following code.\n\n```\n## data\nd <- read.csv(\"linreg.csv\")\n## regression\nm <- lm(y ~ x, data = d)\nsummary(m)\n## visualization\nplot(y ~ x, data = d)\nabline(m)\n```\n\n:::\n\n:::\n::: {.webex-question }\n::: {.webex-check .webex-box}\n\n\n\n**Theory:** Consider a linear regression of `y` on `x`. It is usually estimated with\nwhich estimation technique (three-letter abbreviation)?\n\n\n\nThis estimator yields the best linear unbiased estimator (BLUE) under the assumptions\nof the Gauss-Markov theorem. Which of the following properties are required for the\nerrors of the linear regression model under these assumptions?\n\n\n\n\n**Application:** Using the data provided in [linreg.csv](linreg.csv) estimate a\nlinear regression of `y` on `x`. What are the estimated parameters?\n\nIntercept: \n\nSlope: \n\nIn terms of significance at 5% level:\n\n\n\n\n\n:::\n::: {.webex-solution}\n\n\n**Theory:** Linear regression models are typically estimated by ordinary least squares (OLS).\nThe Gauss-Markov theorem establishes certain optimality properties: Namely, if the errors\nhave expectation zero, constant variance (homoscedastic), no autocorrelation and the\nregressors are exogenous and not linearly dependent, the OLS estimator is the best linear\nunbiased estimator (BLUE).\n\n**Application:** The estimated coefficients along with their significances are reported in the\nsummary of the fitted regression model, showing that `y` increases significantly with `x` (at 5% level).\n\n::: {.cell}\n::: {.cell-output .cell-output-stdout}\n\n```\n\nCall:\nlm(formula = y ~ x, data = d)\n\nResiduals:\n Min 1Q Median 3Q Max \n-0.59250 -0.19501 -0.01624 0.16970 0.58488 \n\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 0.001676 0.025788 0.065 0.948 \nx 0.669237 0.043362 15.434 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.2578 on 98 degrees of freedom\nMultiple R-squared: 0.7085,\tAdjusted R-squared: 0.7055 \nF-statistic: 238.2 on 1 and 98 DF, p-value: < 2.2e-16\n```\n\n\n:::\n:::\n\n**Code:** The analysis can be replicated in R using the following code.\n\n```\n## data\nd <- read.csv(\"linreg.csv\")\n## regression\nm <- lm(y ~ x, data = d)\nsummary(m)\n## visualization\nplot(y ~ x, data = d)\nabline(m)\n```\n\n:::\n\n:::\n:::",
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