statistics

A certain city holds a 100.5 mile running race. The following chart lists the times that a runner arrived at various mileage points along the way. Time (hours) Miles 0 2.498 11.63 4.079 18.11 6.416 27.29 8.153 32.8 8.482 36.56 9.638 43.41 12.061 52.86 13.623 57.44 17.698 72.86 21.343 81.76 22.049 83.78 23.905 91.73 26.595 100.67 a. What was the runner's average speed? b. Graph the data, plotting time on the x-axis and distance on the y-axis. Do the data appear to lie approximately on a straight line? c. Find the equation for the least squares line, fitting distance as a linear function of time. Y =[x+0 d. Calculate the correlation coefficient. Does it indicate a good fit of the least squares line to the data? e. Based on your answer to part (d), what is a good value for the runner's average speed? Compare this with your answer to part (a). Which answer do you think is better? Explain your reasoning. Using a discount travel website, the prices for a one-way flight from one city to various other cities were recorded. The following table gives the distances from the city to 14 selected cities, along with the airfare to each of these cities. N City Distance, Price, x (miles) y (dollars) 800 55 1770 139 1197 237 1236 229 2784 200 1207 216 892 219 95 278 2410 172 2884 156 2706 214 948 245 276 250 Z 2815 156 a. Plot the data. Do the data points lie in a linear pattern? b. Find the correlation coefficient. c. Identify the outlier in the scatterplot. What is the correlation coefficient with this city removed? d. With the outlier removed, find the equation for the least squares line, and use it to find the approximate marginal cost per mile to fly