Question

The data below was collected from manufacturer advertisements of their vehicles horsepower and highway gas mileage...

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.

Homework Answers

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 %

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