CHAPTER 13 Simple Linear Regression

556 CHAPTER THIRTEEN Simple Linear Regression
Testing for the Existence of Correlation
Confidence Interval Estimate for the Mean of Y
Yˆ
± t S h
i n−2
YX i
t =
r − ρ
1 − r
n − 2
Yˆ
− t S h ≤ µ ≤ Yˆ
+ t S h
i n− 2 YX i Y | X = Xi
i n−2
YX i
2
(13.19)
(13.20)
Prediction Interval for an Individual Response, Y
Yˆ
± t S 1 + h
i n−2
YX i
Yˆ
− t S 1+ h ≤ Y ≤ Yˆ
+ t S 1+
h
i n− 2 YX i X= Xi
i n−2
YX i
(13.21)
KEY TERMS
assumptions of regression 529
autocorrelation 534
coefficient of determination 526
confidence interval estimate for the
mean response 546
correlation coefficient 542
dependent variable 512
Durbin-Watson statistic 536
error sum of squares (SSE) 524
equal variance 530
explained variation 524
explanatory variable 513
homoscedasticity 530
independence of errors 529
independent variable 512
least-squares method 516
linear relationship 512
normality 530
prediction interval for an individual
response, Y 547
prediction line 515
regression analysis 512
regression coefficient 516
regression sum of squares (SSR) 524
relevant range 519
residual 530
residual analysis 530
response variable 513
scatter diagram 512
scatter plot 512
simple linear regression 512
simple linear regression equation 515
slope 513
standard error of the estimate 528
total sum of squares (SST) 524
total variation 524
unexplained variation 524
Y intercept 513
CHAPTER REVIEW PROBLEMS
Checking Your Understanding
13.64 What is the interpretation of the Y intercept and the
slope in the simple linear regression equation?
13.65 What is the interpretation of the coefficient of
determination?
13.66 When is the unexplained variation (that is, error
sum of squares) equal to 0?
13.67 When is the explained variation (that is, regression
sum of squares) equal to 0?
13.68 Why should you always carry out a residual analysis
as part of a regression model?
13.69 What are the assumptions of regression analysis?
13.70 How do you evaluate the assumptions of regression
analysis?
13.71 When and how do you use the Durbin-Watson
statistic?
13.72 What is the difference between a confidence interval
estimate of the mean response, µ YX | = Xi
, and a prediction
interval of Y X = Xi
?
Applying the Concepts
13.73 Researchers from the Lubin School of Business at
Pace University in New York City conducted a study on
Internet-supported courses. In one part of the study, four
numerical variables were collected on 108 students in an
introductory management course that met once a week for
an entire semester. One variable collected was hit consistency.
To measure hit consistency, the researchers did the
following: If a student did not visit the Internet site
between classes, the student was given a 0 for that time
period. If a student visited the Internet site one or more
times between classes, the student was given a 1 for that
time period. Because there were 13 time periods, a student’s
score on hit consistency could range from 0 to 13.
The other three variables included the student’s course
average, the student’s cumulative grade point average