1. An American consumer organization is currently examining the relationship among several variables including gasoline mileage as measured by miles per gallon; the horsepower of the cars engine and the weight of the car (in pounds). A sample of 50 recent car models was selected and the results recorded. (provided in auto.xlxs)

(a) Using the sample data attached, calculate the sample mean and standard deviation for the variables: -

1. Miles per gallon (MPG)

2. Horsepower

3. Weight (in pounds)

(b) Is there any evidence of skewness in the data sets? Which data set displays greatest skewness?

(c) Using the sample data on MPG, calculate the sample proportion of vehicles whose fuel economy exceeds 37 mpg and its corresponding standard deviation.

(d) Indicate all possible relationship between the variables and comment on it. (You may use scatter diagram or Karl Pearsons correlation coefficient)

(e) Using the complete data set and using simple ordinary least squares regression formulae develop two models to explain the behavior of gasoline mileage (Miles per gallon) as a function of their-

(i) Horsepower

(ii) Weight

f. Which model best describes the behavior of gasoline mileage? Explain your reasons here.