Final answer:
Determining the significance of the independent variable 'duration' requires the regression model output, which would display stars indicating significance or a p-value indicating whether to reject the null hypothesis. A positive coefficient would indicate a positive relationship but not necessarily significance.
Step-by-step explanation:
The student is asking about performing a linear regression analysis in R and interpreting the significance of the independent variable. In the context provided, the significance of the predictor can be determined by checking if the coefficient for the independent variable is significantly different from zero using a star rating or looking at the p-value. A star (or stars) indicates significance in most standard outputs from statistical software, while a p-value less than the chosen alpha level (usually 0.05) indicates that the independent variable is a significant predictor of the dependent variable.
For the provided question options, the correct answer cannot be determined without the actual output of the regression analysis, as the significance of a variable is indicated by the p-value or stars next to the coefficient, and the positive or negative direction of the relationship is shown by the sign of the coefficient. The appropriate information to determine whether 'duration' is a significant predictor of 'fare' should include either the stars or the p-value from the regression model output.