12. Regression

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.

Given a linear regression equation of the form $y=a+bx$ with $b=3$ and $a=-6$, what is the predicted value of $y$ when $x=4$?

Given the following data points: $(1,2)$, $(2,3)$, $(3,5)$, use the least squares method to find the equation of the regression line in the form $y=a+bx$. Which of the following is the correct regression equation?

Which of the following represents the equation of the least-squares regression line for predicting $y$ from $x$?

The scatterplot below shows a set of data and its least-squares regression line. Based on the graph, which of the following is most likely the equation of the regression line?

A regional sales manager records data on the number of clients a salesperson contacts in a week (x) and the total sales generated that week (y). The data from 10 salespeople is shown below. Find the equation of the regression line and use it to predict sales if the salesperson contacts (a) 6 clients; (b) 40 clients

"In Exercises 9 and 10, identify the explanatory variable and the response variable.

9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight

loss."

2. Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

5. To predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables?

"In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.

7. The y-value of a data point corresponding to x;

a. \hat{y}_i

b. y_i

c. b

d. (\bar{x}, \bar{y})

e. m

f. \bar{y}"