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= |
S_{xy}/(√S_{xx}*S_{yy})
= |
-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 %

We expect a car's highway gas mileage to be related to its city
gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles
in the government's Fuel Economy Guide give the regression
line
highway mpg = 6.785 + (1.033 * city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer to three
decimal places.)
mpg
Say in words what the numerical value of the slope tells us.
Highway...

We expect a car’s highway gas mileage to be related to its city
gas mileage (in mpg). Data for all 12091209 vehicles in the
government’s 2016 Fuel Economy Guide give the regression
line
highway mpg=7.903+(0.993×city mpg)highway mpg=7.903+(0.993×city
mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer rounded
to three decimal places.)
slope:
What does the numerical value of the slope tell you?
Highway gas mileage increases with city gas mileage...

We expect a car's highway gas mileage to be related to its city
gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles
in the government's 2013 Fuel Economy Guide give the
regression line
highway mpg = 6.785 + (1.033 × city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer to three
decimal places.)
____mpg
Say in words what the numerical value of the slope tells us....

We expect a car’s highway gas mileage to be related to its city
gas mileage (in mpg). Data for all 1209 vehicles in the
government’s 2016 Fuel Economy Guide give the regression
line
highway mpg=7.903+(0.993×city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer rounded
to three decimal places.)
slope:
What does the numerical value of the slope tell you?
On average, highway mileage increases by 0.993 mpg for each...

We expect a car’s highway gas mileage to be related to its city
gas mileage (in mpg). Data for all 1209 vehicles in the
government’s 2016 Fuel Economy Guide give the regression
line
highway mpg=7.903+(0.993×city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer rounded
to three decimal places.)
slope:
What does the numerical value of the slope tell you?
On average, highway mileage decreases by 0.993 mpg for each...

The data below is 9 observations of car weight (x) and gas
mileage (y). Calculate the linear correlation coefficient, rr.
Enter your answers to two decimal places.
X
(tons)
Y
(mpg)
2.4
24
3.1
30
2.1
32
2.3
32
2.6
34
1.5
33
0.9
34
1
44
1.4
35

for
a data set of weights (pounds) and highway fuel consumption
amount(mpg) pf six tupes of automobile, the linear correlation
coefficient os found and the p- value is 0.037. write a statement
that interpretes the p- value and includes a conclusion about
linear correlation coefficient that is at least as extreme ____%
which is_____ so there ______sufficient evidence to conclude that
there is a linear correlation between weight and highway fuel
consumption in automobiles.

Question 4: Analysts at a major automobile
company collected data on a variety of variables for a sample of 30
different cars and small trucks. Included among those
data were the EPA highway mileage rating and the horsepower of each
vehicle. The analysts were interested in the
relationship between horsepower (x) and highway mileage (y). Given
below is the Excel output from regressing starting miles per gallon
(MPG) on number of horsepower for a sample of 30
students.
Note: Some of the...

As a follow-up to a report on gas consumption, a consumer
group conducted a study of SUV owners to estimate the mean mileage
for their vehicles. A simple random sample of 92
SUV owners was selected, and the owners were asked to report
their highway mileage. The results that were summarized from the
sample data were
x overbarxequals=19.9
mpg and
s=6.8
mpg. Based on these sample data, compute and interpret a
95%
confidence interval estimate for the mean highway mileage...

Listed below are annual data for various years. The data are
weights (metric tons) of imported lemons and car crash fatality
rates per 100,000 population. Construct a scatterplot, find the
value of the linear correlation coefficient r, and find the
P-value using alpha = 0.05. Is there sufficient evidence to
conclude that there is a linear correlation between lemon imports
and crash fatality rates? Do the results suggest that imported
lemons cause car fatalities?
Lemon_Imports_(x) Crash_Fatality_Rate_(y)
230
15.8
266 ...

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