isds 361A
ISDS 361A
Dr. Huang
Case Study
The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends upon many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for a 2007 model year Camry, the following data show the mileage and sales price for 19 sales (PriceHub website, February 24, 2012). Suppose that you are considering purchasing a previously owned 2007 Camry that has been driven 60,000 miles. What price you would offer to the seller and why?
Miles (1000s) |
Price ($1000s) |
22 |
16.2 |
29 |
16 |
36 |
13.8 |
47 |
11.5 |
63 |
12.5 |
77 |
12.9 |
73 |
11.2 |
87 |
13 |
92 |
11.8 |
101 |
10.8 |
110 |
8.3 |
28 |
12.5 |
59 |
11.1 |
68 |
15 |
68 |
12.2 |
91 |
13 |
42 |
15.6 |
65 |
12.7 |
110 |
8.3 |
Your report should have the following qualities:
1. Your report must be in a genuine report format with problem definition, analysis and final conclusion.
2. All important analysis steps needs to be followed to arrive at the model to be used for prediction. Attach the details of your analysis at the end of your report. Very simplistic analysis with no sufficient details is assigned a near zero credit. Just running excel does not guarantee any credit.
3. The report should including the discussions of the scatter diagram, regression equation, test for significant relationship, coefficient of determination, correlation coefficient, interpretation of the slope of the regression equation, 95% prediction interval and the 95% confidence interval of the mean sales price given mileage.
There are two variables. In this simple linear regression, miles is the independent variable and price is the dependent variable. The miles recorded in the odometer affects its price. I have used the scatter plot graph to show the relationship between two variables. We have collected the price ($1000) and the number of miles (thousands) on the odometer of randomly selected 20 2007 year model Toyota Camry’s. The objective is to find the relationship between the prices of used Toyota Camry’s and the odometer readings. And the goal is to find the price I would offer to the seller for a previously owned 2007 Camry that has been driven 60,000 miles.
The scatter plot diagram shown the slope β1 is negative with a decreasing regression line. The data is negative linear relationship. The estimated regression equation is ŷ=ƅ0+ƅ1x, b0 is 16.47 and b1 is -0.0588. The interpretation is when miles increase, the price decreases. -0.0588 is the marginal revenue. Increase every 1000 miles, decrease $58.8 of value in price.
The hypothesis test H0: β1=0, Ha: β≠0. The p value is greater than α=0.05, we do not reject the null hypothesis.
R Square represents the coefficient of determination. R square is about 0.5 the model is moderate. R is 0.7339 which is pretty close to 1 means that the linear relationship is strong. It looks like a straight-line fits through the points fairly well.
In assumption, I would offer to the seller $12942=-0.0588(60) +16.47 for a pre-owned 2007 Camry that has been driven 60,000 miles.