The owner of a shop selling musical instruments conjectures that the most important variable affecting the sales in the sector (measured in thousands of f) is the distance to the nearest competing music shop (measured in kilometers). In order to test her conjecture, she randomly selected 15 musical instrument shops and measured both the sales and the distance to the nearest competitor. In the process, she also obtained data on the average price of an sold instrument (in f). All data are shown in the table below. Observation Sales (x1000f) Distance (K'm) Price (f) 41.50 0.70 120 2 50.65 5.80 118 3 70.76 7.75 98 4 81.45 8.07 110 5 96.73 7.13 78 6 51.67 6.07 130 7 56.25 6.55 127 8 59.05 6.69 112 9 99.27 10.26 88 10 40.22 4.56 138 11 46.07 2.11 125 12 58.04 7.58 88 13 63.38 9.59 110 14 68.47 6.17 97 15 76.62 7.60 100 [Please turn page] Help the owner to: (a) Plot the data. (b) Determine the estimated regression line to test the conjecture that sales depend on the distance. Give an economic interpretation of the estimated slope (b) coefficient. (c) Determine if distance is a statistically significant variable in estimating sales. (d) Calculate the coefficient of determination. (e) Construct an approximate 95% prediction interval for the sales if the nearest competitor locates at a distance of 3.5 Km. (f) Use both your economics and statistical knowledge to discuss how the model could be improved. Using the available data, propose at least one model that you think it is better than the one used by ANI - the shop owner. Run the model and discuss its results. Discuss briefly if the model is effectively better than the one originally proposed by the shop owner. +