Question

A new online auction site specializes in selling automotive parts for classic cars. The founder of the company believes that the price received for a particular item increases with its age (the age of the car on which the item can be used in years) and with the number of bidders. Use the multiple regression output below to answer the following questions.
Summary measures Multiple R 0.8391 R-Square 0.7041 Adj R-Square 0.6783 StErr of Estimate 148.828
Regression coefficients Coefficient Std Err t-value p-value Constant -1242.986 331.204 -3.7529 0.0010 Age of part 75.017 10.647 7.0459 0.0000 Number of Bidders 13.973 10.443 1.3380 0.1940
a. Use the information above to write out the form of the linear regression model.
b. Interpret each of the estimated regression coefficients of the regression model.
c. Is the founder of the company correct in believing that the price received for the item increases with its age and with the number of bidders? Explain your answer.

Answer 1

Solution :

a). The required linear regression model is

Price = $-1242.986 + 75.017 \times \text{age of part} + 13.973 \times \text{ number of bidders}$

b). The $\text{p-value}$ for the variable "Age of part" is 0.0000

Since the $\text{p-value}$ is less than 0.05, so it is significant to the model.

The p-value for the variable "Number of bidders" is 0.1940

Since $\text{p-value}$  is not less than $0.05$, so it is significant to the model.

c). We cannot say that model is significant because variable " the number of bidders" is not significant.

But as both variables have positive coefficient so as the variable increases the price received for the item also increased.