12. Regression

Given the least squares regression equation $y=a+bx$, what does the coefficient $b$ represent?

In linear regression using the least squares method, the line of best fit for a scatterplot always passes through which pair of points?

In linear regression using the least squares method, which formula correctly represents the slope of the line of best fit for a set of data points $(x,y)$?

In linear regression using the least squares method, what is the expected shape or equation of the calibration plot relating the dependent variable to the independent variable?

In linear regression, the least squares method minimizes which of the following quantities?

In a regression analysis using the least squares method, what is the primary objective when fitting a line to the data?

[DATA] Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL levels. He obtained the following data.

b. Determine the least-squares regression equation from the sample data.

Given a set of data points, the least squares regression line is calculated to best fit the data. Which of the following values is the most likely approximate slope of the line of best fit if the data shows a strong negative linear relationship?

Which of the following is true concerning linear regression using the least squares method?

Given the least squares regression equation $y^{^}=1.202+1.133x$, when $x=3$, what does $y^{^}$ equal?

[DATA] American Black Bears In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the American black bear (Ursus americanus) population in Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable that is thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears. Use the results from Problem 20 in Section 4.2 to answer the following questions:

d. What is the mean weight of American black bears of length 146.0 cm?

Two variables have a bivariate normal distribution. Explain what this means.