Question

In regression, we call Y the response or dependent variable, which is modeled in terms of one or more "independent" variables. The independent variables are further classified as explanatory/causal variables or as predictor variables. Discuss and elaborate on whether or not

• time can be a legitimate explanatory/causal variable,
• whether time can be a legitimate predictor variable
• whether a predictor variable must also be a causal/explanatory variable.

Provide examples to support your arguments.

Answer 1

Time can be legitmate explantory/casual variable

let time be explantory variable & rating be response variable

here is data

Let us find the value of correlation coeffcient using minitab

Step1: Select Stat>Basic Stastics>Correlation

Step 2:In variables select time and rating  

Step 3:Click Ok

Mintab output

Correlation Time,Rating

Pearson correlation of time and rating is 0.541

P-value:0.000

It means that there is positive relationship between time and rating

In time series data time is explanatory variable

Yes Time can also be predictor variable

for example predicting future values with regression  model

For example data set has monthly customer profit(which is my target value) and set of predictor variables (balances of different account) for one year of each customer

Another example Viscosity of resin is dependent on time which depend on season

in winter in night time at lower temperature viscosity of resin automatically increases

In Weather Forecasting time is predictor variable

It is not necessary that predictor variable must also be explanatory variable