Book cover for Stats Data and Models

Stats Data and Models

Richard D. De Veaux, Paul F. Velleman, David E. Bock

ISBN #9780321986498

4th Edition

1,406 Questions

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16,980 Students Helped

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section emphasizes the importance of regression inference in analyzing relationships between variables. It illustrates how to test hypotheses about regression coefficients (especially the slope), construct confidence and prediction intervals, and check essential model assumptions (linearity, independence, constant variability, and normality). Additionally, the section introduces logistic regression as a method for modeling binary outcomes. Overall, understanding standard errors, R-squared, and proper assumption checking is crucial for drawing reliable conclusions from regression analyses.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Analysis of Variance (ANOVA)

A collection of statistical techniques used to compare the means of three or more groups by partitioning total variability into components due to differences among groups (between-group) and within groups.

Example Problems

Example 1

Graduation rates 2013 A prestigious college is interested in factors that might be associated with better graduation rates. The administrators wonder whether there is a relationship between acceptance rates and graduation rates. Before proceeding with their regression inference, what conditions and assumptions must be satisfied? Are they? (Source: US News and World Report National University Rankings October $2013 .$ http://colleges .usnews.rankingsandreviews.com/best-colleges/rankings /national-universities/data/spp' $\mathrm{p} \% 2 \mathrm{~B} 50 / \mathrm{page}+1)$ Response variable is Grad\% R-squared $=75.2 \%$ with $50-2=48$ $s=0.0254$ degrees of freedom $\begin{array}{lclll}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-Ratio } & \text { P-Value } \\ \text { Intercept } & 0.975175 & 0.0074 & 131 & \leq 0.0001 \\ \text { Acceptance \% } & -0.284895 & 0.0236 & -12.1 & \leq 0.0001\end{array}$

Example 2

Shoot to score A college hockey coach collected data from the $2010-2011$ National Hockey League season. He hopes to convince his players that the number of shots taken has an affect on the number of goals scored. The coach performed a preliminary analysis, using the scoring statistics from 293 offensive players who play professional hockey. He predicts Goals from number of Shots (taken for the season). Discuss each of the conditions and assumptions required for him to proceed with the regression analysis. (www.nhl.com) Dependent variable is Goals R-squared $=63.4 \%$ $s=5.13$ with $293-2=291$ degrees of freedom $\begin{array}{lcccc}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-Ratio } & \text { P-Value } \\ \text { Intercept } & -1.77095 & 0.9087 & -1.9488 & 0.052 \\ \text { Shots } & 0.11938 & 0.0053 & 22.460 & <0.0001\end{array}$

Example 3

Graduation rates $2013,$ part II Using the regression output in Exercise 1 , identify the error standard deviation and explain what it means in the context of the problem.

Example 4

Shoot to score another one Using the regression output from Exercise 2 , identify the error standard deviation and explain its meaning with a sentence in context.

Example 5

Graduation rates $2013,$ part III Continuing with the regression of Exercise $1,$ write a sentence that explains the meaning of the standard error of the slope of the regression line, $S E\left(b_{1}\right)=0.0240$.
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Step-by-Step Explanations

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Common Mistakes

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