A marketing manager for a computer manufacturer was interested in whether consumers could evaluate the price of laptops and desktops with different features. An Weeks experiment was devised in which a set of consumers were randomly shown one computer from an inventory and were asked to guess its price. Four computers were used in the study, with list prices of $1,800; $2,500; $3,000; and $4,500. The following table summarizes the findings. Each column represents a different computer, with its price in the first row. The rest of the column contains the various guesses by randomly selected customers. 

a. Explore the possibility of a linear relation between a customer’s guesses and actual prices. Does there seem to be a strong linear relationship, based on a scatter plot and the correlation?
b. Build a linear model to represent a customer’s price guess for a given computer price. What guess would the model predict for a computer that has a list price of $3,600?
c. What is the probability that the intercept term in the model of (a) is actually zero? Build a linear model with an intercept of zero to represent a customer’s price guess for a given computer price. What guess would the model predict for a computer that has a list price of $3,600?
d. What advantages or disadvantages does the model in (b) have?

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Actual price Guesses C1 1,800 1,400 2,300 2,200 3,000 1,000 1,500 1,400 C2 2,500 2,500 2,600 2,400 2,700 2,500 2,600 1,800 2,400 C3 3,000 3,600 3,300 3,600 3,600 3,700 C4 4,500 3,600 5,500 4,900 5,600 4,600 4,300 6,100