The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.) Speed, v 20 40 60 80 100 Reaction Time Distance, R 8.6 17.0 25.3 33.6 42.0 Braking Time Distance, B 2.6 9.3 20.5 36.1 56.2 (a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.) R(v) = (b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance B. (Round numerical values to four decimal places.) B(v) = (c) Determine the polynomial giving the total stopping distance T. (Round numerical values to four decimal places.) T(v) =
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 stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.)
| Speed, v | 20 | 40 | 60 | 80 | 100 |
| Reaction Time Distance, R |
8.6 | 17.0 | 25.3 | 33.6 | 42.0 |
| Braking Time Distance, B |
2.6 | 9.3 | 20.5 | 36.1 | 56.2 |
(a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.)
R(v) =
B(v) =
T(v) =
T'(v) =
Find the rates of change of the total stopping distance for
| T'(40) | = | |
| T'(80) | = | |
| T'(100) | = |
(f) Use the results of this exercise to draw conclusions about the total stopping distance as speed increases.
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Consider the provided table,
| Speed, V | 20 | 40 | 60 | 80 | 100 |
| Reaction time distance, R | 8.6 | 17.0 | 25.3 | 33.6 | 42.0 |
| Braking time distance, B | 2.6 | 9.3 | 20.5 | 36.1 | 56.2 |
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