Question

Scientists believe there is a link between ambient temperature and damage to a head gasket on a car. Using the provided information, draw a scatterplot of the data.

Based on the information, what might the approximate damage index be if the temperature was 10° Celsius?
A) 5
B) 7
C) 10
D) 13

Answer 1

The correct option is D.

Explanation:

The given data table represents the damage index to a head gasket on a car at various temperatures.

From the given table it is clear that the relation between temperature(in degree celsius) and damage index to a head gasket on a car is negative.

Because the value of damage increases as temperature decreases and the value of damage decreases as the temperature increases.

From the given table it is notices that the damage index is 11 at x=12.

Since the relation between temperature and damage index is negative, therefore the damage index would be more than 11 for x=10.

The value of damage deceases exponentially. So the exponential regression line form that data is

`y=ab^x`

Using technology, we get a=116.8 and b=0.805.

`y=116.8(0.805)^x`

At x=10, the value of damage index is

`y=116.8(0.805)^(10)=13.348\approx 13`

Only 13 is more than 11, therefore the correct option is D.

Answer 2

D) 13

Explanation:

A linear regression line crosses the 10 °C line at a damage index of about 11. A quadratic or exponential regression line gives a better fit and a much higher value of damage index at 10 °C. Splitting the difference, we choose answer D) 13.