The following table shows the cost C of traffic accidents, in cents per vehicle-mile, as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s 20 25 30 35 40 45 50 Cost C 1.3 0.4 0.1 0.3 0.9 2.2 5.8 The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled as a quadratic function of vehicular speed s, and the cost per vehicular involvement is roughly a linear function of s, so we expect that C (the product of these two functions) can be modeled as a cubic function of s. (a) Use regression to find a cubic model for the data. (Keep two decimal places for the regression parameters written in scientific notation.) _______ (b) Calculate C(44) and explain what your answer means in practical terms. (Use the model found in part (a). Round your answer to two decimal places.) C(44) = _______ so for a vehicle driving _____ mph at night on urban streets, the cost of a traffic accident will be ______ cents per vehicle mile. (c) At what speed is the cost of traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Use the model found in part (a). Consider speeds between 20 and 50 miles per hour. 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 cost C of traffic accidents, in cents per vehicle-mile, as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets.
| Speed s | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
|---|---|---|---|---|---|---|---|
| Cost C | 1.3 | 0.4 | 0.1 | 0.3 | 0.9 | 2.2 | 5.8 |
The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled as a quadratic function of vehicular speed s, and the cost per vehicular involvement is roughly a linear function of s, so we expect that C (the product of these two
(c) At what speed is the cost of traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Use the model found in part (a). Consider speeds between 20 and 50 miles per hour. Round your answer to the nearest whole number.)
_______mph
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