LC3_2023 - Supervised learning

What is a correlation coefficient?

• It describes the difference in means of two variables

• • It describes the causal relation between two variables

• It is the standardized covariance

• • It describes the degree to which the variation in one variable is related to the variation in another variable

• None of these

Which line through a scatterplot produces the best fit in a linear regression model?

• he line associated with the steepest slope parameter

• • The line that minimizes the sum of the squared deviations of the predicted values (regression line) from the observed values

• The line that minimizes the sum of the squared residuals

• The line that maximizes the sum of the squared residuals

• None of these

Which of the following statements about the adjusted R-squared is TRUE?

• • It increases with every additional variable

• • It increases only with additional variables that add more explanatory power than pure chance

• • It contains a “penalty” for including unnecessary variables

• None of these

When do you use a logistic regression model?

• • When the dependent variable is continuous

• • When the independent and dependent variables are binary

• • When the dependent variable is binary

• None of these

What is the correct way to implement a linear regression model in R? (x = independent variable, y = dependent variable)?

• lm(y~x, data=data)

• lm(x~y + error, data=data)

• lm(x~y, data=data)

• lm(y~x + error, data=data)

• None of these

Considering this output from a bivariate correlation,

• …lower prices cause higher sales.

• …lower prices are associated with higher sales and vice versa.

• None of these

When interpreting the statistical significance of a regression coefficient, the p-value…

• …of 0.05 means that, if the null hypothesis is true (i.e., if the independent variable would NOT affect the outcome), the odds are 19 in 20 of getting a regression coefficient as large or larger than the estimated coefficient

• …of 0.05 means that, if the null hypothesis is true (i.e., if the independent variable would NOT affect the outcome), the odds are 1 in 20 of getting a regression coefficient as large or larger than the estimated coefficient

• …of 0.05 means that the effect is statistically significant at the 5% level.

• …does not tell you anything about the importance of the effect

• …will get smaller, the larger the calculated value of the test statistic (t-value).

In which setting(s) would a regression coefficient be interpreted as “statistically significant”?

• • When the absolute value of the calculated test-statistic (e.g., t-value) exceeds the critical value of the test statistic at your specified significance level (e.g., 0.05)

• • When the test-statistic (e.g., t-value) is lower than the critical value of the test statistic at your specified significance level (e.g., 0.05)

• When the confidence interval associated with the test does not contain zero

• • When the p-value is smaller than your specified significance level (e.g., 0.05)

When interpreting the significance of the coefficients in a regression model, what is the relationship between the test statistic (e.g., t-value) and the p-value?

• The lower the absolute value of the test statistic, the lower the p-value

• The higher the absolute value of the test statistic, the higher the p-value

• There is no connection between the test statistic and the p-value

• The higher the absolute value of the test statistic, the lower the p-value

What does the term overfitting refer to?

• A regression model that fits to a specific data set so poorly, that it will not generalize to other samples

• A regression model that fits to a specific data set so well, that it will generalize to other samples particularly well

• A regression model that has too many predictor variables

• A regression model that fits to a specific data set so well, that it will only predict well within the sample but not generalize to other samples