Question

The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012).

DATA

Miles (1,000s) Price ($1,000s) 22 16.2 29 16.0 36 13.8 47 11.5 63 12.5 77 12.9 73 11.2 87 13.0 92 11.8 101 10.8 110 8.3 28 12.5 59 11.1 68 15.0 68 12.2 91 13.0 42 15.6 65 12.7 110 8.3

(a) Choose a scatter chart below with ‘Miles (1000s)’ as the independent variable. (i) (ii) (iii) (iv) What does the scatter chart indicate about the relationship between price and miles? The scatter chart indicates there may be a linear relationship between miles and price. Since a Camry with higher miles will generally sell for a lower price, a negative relationship is expected between these two variables. This scatter chart is consistent with what is expected.

(b) Develop an estimated regression equation showing how price is related to miles. What is the estimated regression model? Let x represent the miles. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) = + x

(c) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d) How much of the variation in the sample values of price does the model estimated in part (b) explain? If required, round your answer to two decimal places. %

(e) For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. If required, round your answer to the nearest whole number. The best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. The second best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price.

(f) Suppose that you are considering purchasing a previously owned Camry that has been driven 100,000 miles. Use the estimated regression equation developed in part (b) to predict the price for this car. If required, round your answer to one decimal place. Do not round intermediate calculations. Predicted price: $ Is this the price you would offer the seller?

Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

Solution-

(a) Scatter plot shows-

It tells that there may be negative relationship between the two variables.

(b) After running the regression model in the excel, we obtain the following output-

Value of R2 = 0.0364

This low value suggests that linear model is a poor fit.

C) Below is the standardised residuals-

D):-
since p-value for intercept=0.0000<alpha=0.01, so test is significant

hence, there is enough evidence that intercept are significantly different from zero

and p-value for slope = 0.0003<alpha=0.01,so slope test is also significant

hence, there is enough evidence that slope are significantly different from zero

E):

variation is explained by R^2

amd R^2=0.5387

so, 53.87% variation in price is explained by miles

F):

predicted price= 16.4698 - 0.0588*miles(1000s)

now x=100000 or 100(1000s)

so,

predicted price= 16.4698 - 0.0588*100=10.5898(1000s)

so, predicted price=10589.8

the price of car may or may not offer to seller because it depend on other factors(conditions) of car.

but this price is reasonable to offer