Question 1206836: The owner of Maumee Motors wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at Maumee Motors during the last year:
Car Age (years) Selling Price ($ thousands) Car Age (years) Selling Price ($ thousands)
1 8 $9.5 7 6 $10.0
2 13 5.5 8 2 5.5
3 7 9.7 9 1 9.6
4 15 3.6 10 4 3.1
5 9 3.2 11 9 7.0
6 8 4.8 12 1 3.7
a. Determine the correlation coefficient. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)
r =
b. Determine the coefficient of determination. (Round the final answer to 3 decimal places.)
c. Interpret these statistical measures. Does it surprise you that an inverse relationship exists? (Round the final answer to the nearest whole number.)
Weak negative (inverse) correlation between age of car and selling price. So,
percent of the variation in the selling price is explained by the variation in the age of the car.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i put this through the linear regression calculator at
these are the results.
wnasers to your questions are shown below.
a. Determine the correlation coefficient. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)
r = -.1763
b. Determine the coefficient of determination. (Round the final answer to 3 decimal places.)
r^2 = .03107
c. Interpret these statistical measures. Does it surprise you that an inverse relationship exists? (Round the final answer to the nearest whole number.)
r^2 is very small, indicating very little of the data is explained by the relationship between x and y.
r is very weak in a negative direction, indicating very little to no correlation between the values of x and y in a negative direction, i.e. as value of x goes up, value of y goes down.
you would expect that, as the age of the care gets higher, that the value of the car will go down.
this is supported by the correlation, but very weakly.
a very large part of the reason is that the data is insufficiently narrowed down to the point where the data will make sense.
one glaring problem is that the make and model of the car is not considered.
different makes and models of cars start at different cost points.
you can't just grab a car at random without taking this into consideration.
a cheap car's starting value can easily be lower than an expensive car's value after 5 or even 10 years.
the data can be all over the place, as is evident with this sample.
the lack of any discernible correlation is definitely caused by a poor selection of data to be analyzed.
a look at the graph shows that the data is spread far and wide from the regression line.
this indicates very poor correlation between the x and y coordinates.
the high p-value supports this conclusion.
if you just go with the r-value and the r^2-value, there is very strong evidence that there's no real good correlation to be derived from this data.
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