R-squared and s Quiz (100%)

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph. What effect will the circled point have on the slope of the least-squares regression line?

a. It will increase the value of the slope because its residual is a large positive value.

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels (this point is circled on the graph) What effect will the circled point have on the standard deviation of the residuals?

a.This point will increase the value of the standard deviation of the residuals because it has a large positive residual.

The length, x (in inches), and weight, y (in ounces), for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the value for r2 was determined to be 96%. Which of the following is the best interpretation of this value?

b. 96% of the variation in the bass's weight is determined by the variation in the bass's length.

In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. A regression analysis was completed and the value for r2 was 52.1%. Which of the following is the correct interpretation of r2?

b. About 52.1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the correlation?

b. The correlation will be weakened because the point falls outside the pattern of the data.

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The given data list the number of absences and GPAs for 15 randomly selected students. Using technology, what is the value of r2?

c. 0. 32

The length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. The measurements are given in the table. Using technology, what is the value of r2?

c. 0.96

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect will this point have on the value of r2 if it is not included in the data?

c. The value of r2 would increase substantially because this point does not follow the pattern of the data.

The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis. Which of the following represents the standard deviation of the residuals?

c.1.61

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. An analysis is performed on the data for 15 randomly selected students and is displayed in the computer output. Which of the following represents the value of the average residual for a student's GPA?

d.0.691