The table below shows the average stopping distance D, in feet, for a car on dry pavement versus the speed S of the car, in miles per hour. S = speed (mph) 15 25 35 40 60 75 D = stopping distance (feet) 44 85 136 164 304 433 (a) Find a model of stopping distance as a power function of speed. (Round regression parameters to two decimal places.) D = 0.89 × S1.42 D = 0.25 × S1.64 D = 3.42 × S0.98 D = 4.63 × S1.23 D = 1.24 × S0.85 (b) If speed is doubled, how is stopping distance affected? (Use the model found in part (a). Round your answer to two decimal places.) What is the stopping distance is multiplied by?
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 table below shows the average stopping distance D, in feet, for a car on dry pavement versus the speed S of the car, in miles per hour.
| S = speed (mph) | 15 | 25 | 35 | 40 | 60 | 75 |
|---|---|---|---|---|---|---|
| D = stopping distance (feet) | 44 | 85 | 136 | 164 | 304 | 433 |
(b) If speed is doubled, how is stopping distance affected? (Use the model found in part (a). Round your answer to two decimal places.)
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