Consider a train that runs from Seattle to Los Angeles. The mean travel time from one stop to the next is 130 minutes, with a standard deviation of 114 minutes. The mean distance traveled from one stop to the next is 106 miles with a standard deviation of 100 miles. The correlation between travel time and distance is 0.631. 360- 300- 240 Travel Time (minutes) 180 120 60 100 200 300 Distance (miles) (a) Write the equation of the regression line for predicting travel time. (Let y represent travel time in minutes and let x represent distance traveled in miles.) 9 = (b) Interpret the slope in this context. For each mile increase in distance traveled, we would expect travel time to increase on average by minutes. Interpret the intercept in this context. When the distance traveled is 0 miles, the travel time is expected to be on average minutes. (c) Calculate R" of the regression line for predicting travel time from distance traveled for the train. (Round your answer to three decimal places.) R2 = Interpret R in the context of the application. (Give your answer as a percent. Round your answer to one decimal place.) Approximately % of the variation in travel time is accounted for by the model. (d) The distance between Santa Barbara and Los Angeles is 103 miles. Use the model to estimate the time (in minutes) it takes for the train to travel between these two cities. (Round your answer to the nearest integer.) min (e) It actually takes the train about 161 minutes to travel from Santa Barbara to Los Angeles. Calculate the residual (in minutes). (Round your answer to the nearest integer.) min Explain the meaning of this residual value. O The model overestimated the train's travel time. O The model accurately estimated the train's travel time. O The model underestimated the train's travel time. (f) Suppose the train company is considering adding a stop for the train 500 miles away from Los Angeles. Would it be appropriate to use this linear model to predict the travel time from Los Angeles to this point? Yes, this model is valid for train trips. O No, this value is outside the realm of the the original data