A streaming service studies whether subscription plan is related to weekly viewing time. The observational units are individual subscribers selected at random. For each subscriber, the service records plan code (1 = Basic, 2 = Standard, 3 = Premium), total hours watched last week, and device type most used. The goal is to see if the plan helps explain variation in hours watched. Which classification is correct for plan code and hours watched?
- Plan code: quantitative explanatory; hours watched: quantitative response
- Plan code: categorical explanatory; hours watched: quantitative response (correct answer)
- Plan code: categorical response; hours watched: quantitative explanatory
- Plan code: quantitative response; hours watched: categorical explanatory
- Plan code: categorical explanatory; hours watched: categorical response
Explanation: This question tests understanding of coded categorical variables. The goal states we want 'to see if the plan helps explain variation in hours watched,' making plan the explanatory variable and hours watched the response. Although plan code uses numbers (1, 2, 3), these are just labels for categories (Basic, Standard, Premium) - the numbers don't have mathematical meaning, so plan code is categorical, not quantitative. Hours watched last week is a numerical measurement that can take many values, making it quantitative. Therefore, plan code is a categorical explanatory variable and hours watched is a quantitative response variable. A common mistake is thinking any variable with numbers must be quantitative, but coded categories remain categorical.