A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? 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) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. 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 = (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 hou
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? 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) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. 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 = (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 hou
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:
y = ?0 + ?1x + ?
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) |
|---|---|
| 1,254 | 35 |
| 1,330 | 40 |
| 1,228 | 30 |
| 1,334 | 45 |
| 1,351 | 50 |
| 1,126 | 25 |
In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
ŷ = b0 + b1x + b2x2
(a)
Develop an estimated regression equation for the data of the form
ŷ = b0 + b1x + b2x2.
(Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.)ŷ =
(b) Use ? = 0.01 to test for a significant relationship.
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 =
(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
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