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.
%%
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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
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