We record data on the population of a particular country from to . A scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is,
log ( population) (years).
Based on this equation, the population of the country in the year 2020 should be about
The population of the country in the 2020 should be about . The correct option is (c).
The population of the country in the year 2020 should be about log (population).
Putting the year with 2020 :
Taking the exponential
Suppose that the relationship between a response variable y and an explanatory variable x is modelled by . Which of the following scatterplots would approximately follow a straight line?
(a) A plot of y against x
(b) A plot of y against log x
(c) A plot of log y against x
(d) A plot of log y against log x
(e) None of (a) through (d)
The swinging pendulum Refer to Exercise 33. Here is Minitab output from separate regression analyses of the two sets of transformed pendulum data:
Do each of the following for both transformations.
(a) Give the equation of the least-squares regression line. Define any variables you use.
(b) Use the model from part (a) to predict the period of a pendulum with length of centimeters. Show your work.
(c) Interpret the value of s in context
Random assignment is part of a well-designed comparative experiment because
(a) It is more fair to the subjects.
(b) It helps create roughly equivalent groups before treatments are imposed on the subjects.
(c) It allows researchers to generalize the results of their experiment to a larger population.
(d) It helps eliminate any possibility of bias in the experiment.
(e) It prevents the placebo effect from occurring
Students in a statistics class drew circles of varying diameters and counted how many Cheerios could be placed in the circle. The scatterplot shows the results.
The students want to determine an appropriate equation for the relationship between diameter and the number of Cheerios. The students decide to transform the data to make it appear more linear before computing a least-squares regression line. Which of the following single transformations would be reasonable for them to try?
I. Take the square root of the number of Cheerios.
II. Cube the number of Cheerios.
III. Take the log of the number of Cheerios.
IV. Take the log of the diameter.
(a) I and II
(b) I and III
(c) II and III
(d) II and IV
(e) I and IV
Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data
on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Some
regression output for these data is shown below.
Which of the following represents a 95% confidence interval for the true slope of the least-squares regression line relating the weight of a bear and its neck girth?
94% of StudySmarter users get better grades.Sign up for free