The table below gives a random sample of engine output in horsepower compared to vehicle price in thousands of dollars. Use this data set to answer the questions below.

Horsepower: 115, 98, 147, 120, 230, 75, 86, 173, 175

Price: 18.4, 16.3, 24.0, 19.0, 40.2, 13.6, 14.1, 31.7, 23.3

a. Is there a linear relationship between the horse power and price ? Explain your answer by drawing a rough sketch of the relationship and define the strength and the direction of this relationship.

b. Find the linear correlation coefficient,r, for this data set.

c. Find the equation for the regression line that predicts the vehicle price as a function of the engine output in horsepower.

d. Predict the vehicle price for a vehicle that has an engine output of 160 horsepower.

e. Several factors influence a vehicle's price in addition to engine output. The Hyundai Elantra (not included in the table above) has an engine output of 129 horsepower and a price of $15,000. Does your model under- or over-predict the price of this vehicle?