Question

The mayor of a city attempted to reduce traffic congestion by introducing a charge. The charge was set at $4.00 for the first year and then increased by $2.00 each year. For each of the first eight years the city officials recorded the average number of vehicles entering the city per day. The charge is given by $ x and the average number of vehicles entering per day denoted by y million. The data is summarized as follows: n=8 ; sum x =88; sum x2=1140; sum y=16.3; sum y2=34.35; sum xy=169 Calculate the product moment correlation coefficient for this data. Calculate the equation of a suitable regression line giving a reason for your choice. Use your equation to estimate the average number of vehicles that will enter the city per day when the charge is $18

Answer 1

Let , X be the charge and Y be the average number of vehicles enter the per day.

From the given data :

a) The product momnet correlation coefficient for this data is ,

b) The regression equation is ,

Where , 'a' be the intercept of the regression equation and 'b' be the slpoe of the regression equation.

Therefore ,

Now , For , x=$18

Therefore ,

Therefore , the average 1.6082 million of vehicles that will enter the city per day when the charge is $18.