(b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. Hgib; = b2 = 0 O Ho: bo = bị = b2 = 0 H3: One or more of the parameters is not equal to zero. %3D O Ho: bq = b2 = o Hg: One or more of the parameters is not equal to zero. O Họ: One or more of the parameters is not equal to zero. Hgi bo = b1 = b2 = 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 =

Linear Algebra: A Modern Introduction
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Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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(b) Use a = 0.01 to test for a significant relationship.
State the null and alternative hypotheses.
: One or more of the parameters is not equal to zero.
Ho:
Ha: b1 = b2 :
= 0
O Ho: bo = b1 = b2
H: One or more of the parameters is not equal to zero.
%3D
= 0
Ho:b1 = b2
= 0
%D
H: One or more of the parameters is not equal to zero.
Ho: One or more of the parameters is not equal to zero.
Hai bo = b1 = b2 = 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?
Do not reject Ho. We cannot conclude that the relationship is significant.
Do not reject Ho. We conclude that the relationship is significant.
Reject Ho. We cannot conclude that the relationship is significant.
Reject Ho. We 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
Transcribed Image Text:(b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. : One or more of the parameters is not equal to zero. Ho: Ha: b1 = b2 : = 0 O Ho: bo = b1 = b2 H: One or more of the parameters is not equal to zero. %3D = 0 Ho:b1 = b2 = 0 %D H: One or more of the parameters is not equal to zero. Ho: One or more of the parameters is not equal to zero. Hai bo = b1 = b2 = 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? Do not reject Ho. We cannot conclude that the relationship is significant. Do not reject Ho. We conclude that the relationship is significant. Reject Ho. We cannot conclude that the relationship is significant. Reject Ho. We 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
A statistical program is recommended.
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:
y = Bo + B1x + E
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.
Vehicle Speed
(x)
Traffic Flow
(y)
1,255
35
1,329
40
1,224
30
1,335
45
1,349
50
1,123
25
In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
ŷ = bo + bqx + b2x²
(a) Develop an estimated regression equation for the data of the form ŷ = b, + b,x + b,x. (Round bo to the nearest integer and b, to two decimal places and b, to three decimal places.)
ŷ =
(b) Use a = 0.01 to test for a significant relationship.
State the null and alternative hypotheses.
Ho: One or more of the parameters is not equal to zero.
Hai b1 = b2
= 0
Hoibo = b1 = b2
= 0
%D
: One or more of the parameters is not equal to zero.
Ho: b, = b, = 0
Transcribed Image Text:A statistical program is recommended. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = Bo + B1x + E 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. Vehicle Speed (x) Traffic Flow (y) 1,255 35 1,329 40 1,224 30 1,335 45 1,349 50 1,123 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = bo + bqx + b2x² (a) Develop an estimated regression equation for the data of the form ŷ = b, + b,x + b,x. (Round bo to the nearest integer and b, to two decimal places and b, to three decimal places.) ŷ = (b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. Ho: One or more of the parameters is not equal to zero. Hai b1 = b2 = 0 Hoibo = b1 = b2 = 0 %D : One or more of the parameters is not equal to zero. Ho: b, = b, = 0
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