Wisconsin is an important milk-producing state. Some people might argue that because of transportation costs, the cost of milk increases with the distance of markets from Wisconsin. Suppose the milk prices in eight cities are as follows.
Cost of Milk
(per gallon) Distance from Madison
(miles)
$2.64 1,245
2.31
425
2.45 1,346
2.52 973
2.19 255
2.55 865
2.40 1,080
2.37 296
*Do not round the intermediate values. Round your answers to 5 decimal places, the tolerance is +/-0.00005.
**Do not round the intermediate values. Round your answers to 4 decimal places, the tolerance is +/-0.005.
a. Use the prices along with the distance of each city from Madison,Wisconsin, to develop a regression line to predict the price of a gallon of milk by the number of miles the city is from Madison.
y Overscript ^ EndScripts= * plus * x
b. Use the data and the regression equation to compute residuals for this model.
Cost of Milk
(per gallon) Distance from Madison
(miles) (y minus y Overscript ^ EndScripts)
$2.64 1,245 **
2.31
425 **
2.45 1,346 **
2.52 973 **
2.19 255 **
2.55 865 **
2.40 1,080 **
2.37 296 **
c. Sketch a graph of the residuals in the order of the x values.
A.
B.
C.
D.
d. Comment on the shape of the residual graph.