Question
In: Statistics and Probability
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 the correlation coefficient. Round your final answer to
four decimal places.
r=r=
2. Write the regression equation below. Round all numbers to four
decimal places.
ˆy=y^=
3. 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.
4. What percentage of variation in highway gas mileage (mpg) can be
explained by horsepower? Round your final answer to two decimal
places.
%%
License
Solutions
Expert Solution
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 57.987438 - 0.11849951 x
Sample size: 7
R (correlation coefficient) = -0.90396077
R-sq = 0.81714508
Estimate of error standard deviation: 5.4656445
Parameter estimates:
| Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
|---|---|---|---|---|---|---|
| Intercept | 57.987438 | 7.1042425 | ? 0 | 5 | 8.1623675 | 0.0004 |
| Slope | -0.11849951 | 0.0250689 | ? 0 | 5 | -4.7269528 | 0.0052 |
Analysis of variance table for regression
model:
| Source | DF | SS | MS | F-stat | P-value |
|---|---|---|---|---|---|
| Model | 1 | 667.4908 | 667.4908 | 22.344082 | 0.0052 |
| Error | 5 | 149.36635 | 29.87327 | ||
| Total | 6 | 816.85714 |
Predicted values:
| X value | Pred. Y | s.e.(Pred. y) | 95% C.I. for mean | 95% P.I. for new |
|---|---|---|---|---|
| 225 | 31.325049 | 2.3676322 | (25.238857, 37.411241) | (16.013582, 46.636516) |
Hence,
1. Correlation coefficient = -0.9040
2. Regression equation:
= 57.9874 - 0.1185x
3. Predicted gas mileage = 31.3250
4. Percent of variation explained = 81.71%
orchestra answered 2 years agoRelated Solutions
Use the data below, showing a summary of highway gas mileage for several observations, to decide...
Use the data below, showing a summary of highway gas mileage for several observations, to decide if the average highway gas mileage is the same for midsize cars, SUV’s, and pickup trucks. Test the appropriate hypotheses at the α = 0.01 level.
n Mean Std. Dev.
Midsize 31 25.8 2.56
SUV’s 31 22.68 3.67
Pickups 14 21.29 2.76
City Mileage, Highway Mileage. We expect a car's highway gas mileage to be related to its...
City Mileage, Highway 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 x city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? Say in words what the
numerical value of the slope tells you.
(b) What is the...
1. The data below is the city gas mileage for a sample of hybrid cars, as...
1. The data below is the city gas mileage for a sample
of hybrid cars, as reported by the Environmental Protection Agency
in 2007.
30, 36, 33, 27, 31, 25, 28, 31, 45 mpg
Construct and interpret a 95% confidence interval for
the population mean for the miles per gallon of hybrids. You may
assume that the population of gas mileage normally distributed with
no outliers. Answer the following:
a What is...
4. In a recent publication, it was reported that the average highway gas mileage of tested...
4. In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 33.2 mpg with
a standard deviation of 2.5 mpg, with the mileages approximately
normally distributed.
H0 : µ = 33.2
Ha : µ < 33.2
Part a: Describe a Type II error in the context of the
hypothesis test.
Part b: If a simple random sample of 100 cars is selected, what
values of the sample mean ¯x...
4. In a recent publication, it was reported that the average highway gas mileage of tested...
4. In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 33.2 mpg with
a standard deviation of 2.5 mpg, with the mileages approximately
normally distributed.
H0 : µ = 33.2
Ha : µ < 33.2
Part a: Describe a Type II error in the context of the
hypothesis test.
Part b: If a simple random sample of 100 cars is selected, what
values of the sample mean ¯x...
In a recent publication, it was reported that the average highway gas mileage of tested models...
In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 33.5 mpg. A
consumer group conducts its own tests on a simple random sample of
12 cars of this model and finds that the mean gas mileage for their
vehicles is 31.6 mpg with a standard deviation of 3.4 mpg.
a) Choose an appropriate significance test for the consumer
group to perform to test the publication's assertion.
b) The...
In a recent publication, it was reported that the average highway gas mileage of tested models...
In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 33.2 mpg with
a standard deviation of 2.5 mpg, with the mileages approximately
normally distributed.
H0 :μ=33.2
Ha :μ<33.2
Part a: Describe a Type II error in the context of the
hypothesis test.
Part b: If a simple random sample of 100 cars is selected, what
values of the sample mean x ̄ would represent sufficient evidence
to reject...
The data provided give the gasoline mileage (in miles per gallon) based on the horsepower of...
The data provided give the gasoline mileage (in miles per
gallon) based on the horsepower of a car's engine and the weight
of the car (in pounds). Using the data provided, determine the
VIF for each independent variable in the model. Is there reason to
suspect the existence of collinearity?
Determine the VIF for each independent variable in the
model.
MPG
Horsepower
Weight
15.8
185
4,758
19.7
106
3,534
20.3
141
3,220
18.8
172
4,466
17.3
166
4,293
27.5
75...
You are asked to analyze the below speed data collected on a highway on different days...
You are asked to analyze the below speed data collected on a
highway on different days of the week for similarity. Use ANOVA
(analysis of variance) to support your conclusion by performing the
following tasks:
Sample 1 (mph)
Sample 2 (mph)
Sample 3 (mph)
50
45
55
55
50
60
50
55
50
50
60
45
60
40
40
State your null hypothesis (H0) and alternative hypothesis
(H1)
State your assumed level of significance (αα)
Calculate mean for sample 1...
You are asked to analyze the below speed data collected on a highway on different days...
You are asked to analyze the below speed data collected on a
highway on different days of the week for similarity. Use ANOVA
(analysis of variance) to support your conclusion by performing the
following tasks:
Sample 1 (mph)
Sample 2 (mph)
Sample 3 (mph)
50
45
55
55
50
60
50
55
50
50
60
45
60
40
40
State your null hypothesis (H0) and alternative hypothesis
(H1)
State your assumed level of significance (αα)
Calculate mean for sample 1...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Discuss the differences among the terms cultural awareness, cultural sensitivity, cultural relevancy, cultural competence, and cultural...
- 1- Suppose you were tasked with developing the customer service qualities required for an external customer...
- History of Present Illness MDJ is a 50-year-old woman whose routine mammogram showed a 2.3 -...
- For a spherical thermal reactor with a water moderator in a homogeneous mixture, what is the...
- How do autobiographical memories change across the lifespan? That is, what is the relationship between one’s...
- Create a Binary Search Tree with the following elements in the order mentioned below: 5, 85,...
- write a MIPS program to ask user to input the number of elements of array
ADVERTISEMENT