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 2.501 11.67 4.01 17.92 6.438 27.67 8.063 33.0 8.641 36.32 9.793 43.78 11.982 52.02 13.547 57.32 17.582 72.19 21.393 80.99 22.357 85.79 23.994 91.91 26.811 99.84 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 56 1771 142 C 1197 236 1239 226 2784 198 1205 216 G 894 216 I 95 278 2409 170 2886 157 2704 217 947 249 2761 248 N 2815 153 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