Download Questions on Nissan Z Cars with Answers - Statistical Methods | STA 2023 and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity!
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Age in Years
Price ($100)
Nissan Z cars: does the age affect the price? KEY
The following are data on age and price for a sample of Nissan Z’s. The data were obtained from the Asian Import edition of the Auto Trader magazine. Ages are in years; prices are in hundreds of dollars, rounded to the nearest hundred dollars.
Car Age Price($100s) 1 5 85 2 4 103 3^6 4 5 82 5^5 6 5 98 7 6 66 8 6 95 9 2 169 10 7 70 11 7 48
a. Make a scatterplot of these data and describe it below.
ANSWER:
Form: Linear Strength: Strong Association: Negative As the Nissan Z increases in age, its price decreases. Outliers: None Influential Observation: One (2, 169)
b. Find the least squares regression line.
ANSWER: ᡷ㕈 㐄 ㎘20.261261ᡶ ㎗ 195.
c. Predict the value of this type of car that is 6 years old.
ANSWER:
I predict that a 6-year-old Nissan Z will be worth about $7,390.09.
d. Predict the value of this type of car that is 12 years old.
ANSWER:
ᡷ㕈 㐄 ㎘20.261261䙦12䙧 ㎗ 195. 㐄 ㎘47.6667 $ I predict that a 12-year-old Nissan Z will be worth about ㎘$4,766.67. But this does not make any sense! (See the answer to the next question.)
e. Consider the two predictions in parts c and d. Which one is an example of extrapolation and why?
ANSWER:
Part d is an example of extrapolation. This is because we are making a prediction using an input of 12 years which is outside the spread of the given Age data: 2 to 7 years. Not surprisingly, this gave us an unrealistic prediction. Note that the unrealistic prediction is not the extrapolation, but rather the result of extrapolating. Moreover, extrapolating can sometimes lead to realistic results such as with predicting the value of an 8-year-old car (as you can check for yourself). The farther away the input we use from the spread of the given x-data, the more likely our prediction will be unreliable.
f. Interpret what the vertical intercept of the regression line means.
ANSWER:
ᡷ㕈 㐄 ㎘20.261261䙦0䙧 ㎗ 195. 㐄 195.468468 $ Therefore, the vertical intercept is (0, 195.468468) (x, ᡷ㕈) (Age in Years, Predicted Price in $100)
Thus, a 0-year-old Nissan Z’s price is predicted to be 195.468468 $100. In other words, a brand new Nissan Z is predicted to be worth about $19,546.85.
