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Chapter 4: Q. 4.39 (page 173)

Fill in the blanks.

a. In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.

b. In regression analysis, an_______ is a data point where removal causes the regression equation to change considerably:

Short Answer

Expert verified

(a) Outlier

(b) Influential observation.

Step by step solution

01

Part (a) Step 1: Given information

In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.

02

Part (a) Step 2: Explanation

An outlier is an observation with a significant residual in comparison to the other observations in the data collection. Outliers and influential points must be identified as part of the regression analysis.

In the context of the regression, an outlier is a statistic that is far from the trend line when related to other observations.

03

Part (b) Step 1: Given information

In regression analysis, an________ is a data point where removal causes the regression equation to change considerably:

04

Part (b) Step 2: Explanation

An influential observation is one that would significantly alter the conclusion of a statistical computation if it were removed from the dataset. In regression analysis, an influential observation is one whose removal has a significant impact on parameter estimations.

The grid cell is an influential observation, and its removal can cause the regression analysis to vary significantly in the linear relationship.

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Most popular questions from this chapter

A measure of the total variation in the observed values of the response variable is the------.

The mathematical abbreviation for it is----.

The coefficient of determination of a set of data points is 0.70yand the slope of the regression line is -3.58. Determine the linear correlation coefficient of the data.

Graduation Rates. Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 years and what influences it is a concern in U.S. colleges and universities.

US News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a function of the per centage of freshmen in the top 10% of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).

a. Draw a scatterplot of the data.

b. Is finding a regression line for the data reasonable? Explain your answer.

c. Determine the regression equation for the data, and draw its graph

on the scatterplot you drew in part (a).

d. Describe the apparent relationship between student-to-faculty

ratio and graduation rate.

e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate?

f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17.

g. Identify outliers and potential influential observations

Age and Price of Orions. In Table 4.2, we provided data on age and price for a sample of 11Orions between 2and 7years old. On the Weiss Stats site, we have given the ages and prices for a sample of 31Orions between 1and 11years old.

a. Obtain a scatterplot for the data.

b. Is it reasonable to find a regression line for the data? Explain your answer.

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See all solutions

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