Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, spent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. (a) Construct a power model of driving time in minutes as a function of the population measured in thousands. (Round regression parameters to two decimal places.) T = 6.84 × N0.87 T = 1.26 × N1.45 T = 3.40 × N0.18 T = 2.47 × N1.53 T = 4.53 × N0.26 (b) Is average driving time in Pittsburgh more or less than would be expected from its population? (Use the model found in part (a).) more than expected less than expected (c) If you wish to move to a smaller city to reduce your average driving time to work by 30%, how much smaller should the city be? (Use the model found in part (a). Round your answer to two decimal places.) %
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.
Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, spent by residents driving to work.
| City | Population N | Driving time T |
|---|---|---|
| Los Angeles | 6489 | 16.8 |
| Pittsburgh | 1804 | 12.6 |
| Washington | 1808 | 14.3 |
| Hutchinson | 38 | 6.1 |
| Nashville | 347 | 10.8 |
| Tallahassee | 48 | 7.3 |
An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population.
An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population.
(b) Is average driving time in Pittsburgh more or less than would be expected from its population? (Use the model found in part (a).)
(c) If you wish to move to a smaller city to reduce your average driving time to work by 30%, how much smaller should the city be? (Use the model found in part (a). Round your answer to two decimal places.)
%
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
