Question

The data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage (mpg.). Use this data to answer the following questions.

x	158	250	340	350	390	190	220
y	33	28	15	17	11	35	42

1. Find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg). Record the p-value below. Round to four decimal places.

p-value=

2. Is there a linear correlation between horsepower and highway gas mileage (mpg)?

3. If there is a linear correlation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places.

r=

4. If there is a linear correlation, write the regression equation below. Otherwise, leave it blank. Round all numbers to four decimal places.
ˆy=

5. Using the data shown above, predict the the highway gas mileage (mpg) for a car that has a horsepower of 225. Round your final answer to two decimal places.

6. If there is a linear correlation, what percentage of variation in highway gas mileage (mpg) can be explained by horsepower? If there is not a linear correlation, leave it blank. Round your final answer to two decimal places.

Answer 1

appltying regression on above data from excel: data- data analysis:

1)

p-value= 0.0052

2) Is there a linear correlation between horsepower and highway gas mileage (mpg) : yes since p value is less than 0.05

3)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

-0.9040

4)

y^ = -0.1185x+57.9874

5)

predicted value=57.9874+225*-0.1185=31.33

6)

percentage of variation in highway gas mileage (mpg) can be explained by horsepower =r^2*100=81.71 %