4. Exploring Relationships in Data Online Quiz Questions

A researcher records students' hours of sleep and class standing. Which display and summary are most appropriate for examining the relationship between these variables?

True or false: In an observational study, labeling one variable as the explanatory variable proves that changing it causes the response variable to change.

When constructing a scatterplot to study how study hours relate to exam score, how should the variables be placed?

A sample has correlation r = 0.80. What is the coefficient of determination, r², expressed as a decimal?

True or false: A positive residual means that the observed response lies above the regression line's predicted value.

Which features should be examined when describing a scatterplot? Select all that apply.

For the model predicted exam score = 58 + 4.2(hours studied), what is the predicted average increase in exam-score points for each additional hour studied?

When is it appropriate to give a substantive interpretation of the intercept in a simple linear regression model?

Which are possible sources of a statistical association? Select all that apply.

A sample compares college students' hours of sleep across first-year, sophomore, junior, and senior groups. Describe an appropriate analysis and explain what conclusion would and would not be justified from an observed difference among the groups.

A sample has r = 0.80. Which interpretation of r² = 0.64 is most appropriate?

A researcher records annual income and region for a sample of households. Which display is most appropriate for comparing the distribution of income across regions?

A study uses study hours to explain or predict exam score. In a scatterplot of these two quantitative variables, how should the axes be assigned?

A scatterplot shows a clear U-shaped pattern, but the sample correlation is close to zero. Which conclusion is most appropriate?

A fitted model is predicted exam score = 58 + 4.2(study hours). What does the value 4.2 represent?

True or false: If an observational study finds that students who study more tend to earn higher scores, the study proves that increasing study time caused the higher scores.

A sample has correlation $r=0.80$ between house size and annual energy use. What is the coefficient of determination, $r^2$? Enter the decimal value.

For one observation, the observed response is 42 and the regression model predicts 45. What is the residual, defined as observed response minus predicted response? Enter the numerical value.