The following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s Accident rate R 20 1600 25 700 30 350 35 350 40 800 45 1200 (a) Use regression to find a quadratic model for the data. (Round the regression parameters to two decimal places.) R = (b) Calculate R(55). (Round your answer to two decimal places.) R(55) = Explain what your answer means in practical terms. Commercial vehicles driving at night on urban streets at _______ miles per hour have traffic accidents at a rate of ________ per 100,000,000 vehicle miles. (c) At what speed is vehicular involvement in traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Round your answer to the nearest whole number.) mph
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.
The following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a
| Speed s | Accident rate R |
|---|---|
| 20 | 1600 |
| 25 | 700 |
| 30 | 350 |
| 35 | 350 |
| 40 | 800 |
| 45 | 1200 |
(b) Calculate
Explain what your answer means in practical terms.
(c) At what speed is vehicular involvement in traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Round your answer to the nearest whole number.)
mph
Quadratic model for the given data is as follows:
The general equation for a quadratic regression model is:
where 
is the intercept,
is the coefficient of variable X,
is the coefficient of x-square
Step by step
Solved in 2 steps with 7 images
