Question

A statistical program is recommended.

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

* y* =

where

*y*= traffic flow in vehicles per hour*x*= vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

Traffic Flow ( y) |
Vehicle Speed ( x) |
---|---|

1,257 | 35 |

1,328 | 40 |

1,225 | 30 |

1,333 | 45 |

1,348 | 50 |

1,122 | 25 |

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

*ŷ* = *b*_{0} +
*b*_{1}* x* +

(a) Develop an estimated regression equation for the data of the
form *ŷ* = *b*_{0} +
*b*_{1}* x* +

*ŷ* =

(b) Use *α* = 0.01 to test for a significant
relationship. State the null and alternative hypotheses.

*H*_{0}: One or more of the parameters is not
equal to zero.

*H*_{a}: *b*_{0} =
*b*_{1} = *b*_{2} = 0

*H*_{0}: *b*_{1} =
*b*_{2} = 0

*H*_{a}: One or more of the parameters is not equal
to zero.

*H*_{0}: *b*_{0} =
*b*_{1} = *b*_{2} = 0

*H*_{a}: One or more of the parameters is not
equal to zero.

*H*_{0}: One or more of the parameters is not
equal to zero.

*H*_{a}: *b*_{1} =
*b*_{2} = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the *p*-value. (Round your answer to three decimal
places.)

*p*-value =

What is your conclusion?

Reject *H*_{0}. We conclude that the relationship
is significant.

Do not reject *H*_{0}. We conclude that the
relationship is significant.

Do not reject *H*_{0}. We cannot conclude that
the relationship is significant.

Reject *H*_{0}. We cannot conclude that the
relationship is significant.

(c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)______ vehicles per hour

Answer #1

A highway department is studying the relationship between
traffic flow and speed. The following model has been
hypothesized:
y = β0 +
β1x + ε
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour.
The following data were collected during rush hour for six
highways leading out of the city.
Traffic Flow
(y)
Vehicle Speed
(x)
1,257
35
1,331
40
1,227
30
1,336
45
1,349
50
1,125
25
In working further with this...

A highway department is studying the relationship between
traffic flow and speed. The following model has been
hypothesized.
y = B0 + B1x + e
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour
The following data were collected during rush hour for six
highways leading out of the city.
Traffic Flow ( )
Vehicle Speed ( )
1294
40
1332
45
1300
40
1233
30
1334
45
1129
25
a. Develop an...

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2.3x2 +
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1,790.
(a)
At α = 0.05, test the significance of the relationship
among the variables.
State the null and alternative hypotheses.
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In a regression analysis involving 30 observations, the
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State the null and alternative hypotheses.
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1,800.
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equal to zero.
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Consider the following data for two variables, x and
y.
x
22
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y
13
22
34
34
41
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b1x. (Round
b0 to one decimal place and
b1 to three decimal places.)
ŷ =
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In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,550 and SSE =
590.
(a)
At α = 0.05, test whether
x1
is significant.
State the null and alternative hypotheses.
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 = 0
Ha: β1 ≠ 0
H0: β0 = 0
Ha:...

In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,600 and SSE =
550.
(a) At α = 0.05, test whether
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State the null and alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠
0H0: β0 ≠ 0
Ha: β0 =
0 H0:
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Ha: β1 =
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Find the value of...

In a regression analysis involving 27 observations, the
following estimated regression equation was developed. ŷ =
25.2 + 5.5x1 For this estimated
regression equation SST = 1,550 and SSE = 530.
(a) At α = 0.05, test whether
x1 is significant.State the
null and alternative hypotheses.
H0: β1 ≠ 0
Ha: β1 = 0
H0: β0 ≠ 0
Ha: β0 =
0
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In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,600 and SSE =
550.
(a) At α = 0.05, test whether
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