Exam 1 Review
Data referenced throughout review

The Federal Trade Commission annually
rates varieties of domestic cigarettes
according to their tar, nicotine, and carbon
monoxide content. The United States
Surgeon General considers each of these
substances hazardous to a smoker's health.
Past studies have shown that increases in
the tar and nicotine content of a cigarette are
accompanied by an increase in the carbon
monoxide emitted from the cigarette smoke.
Foundations (1)

Are sex, ethnicity and political party
categorical or quantitative variables?
Foundations (2)
The two branches of statistics are:
______________ and ______________.

Foundations (3)

Is oF an interval or ratio measurement?
Explain.
Foundations (4)

Explain how a statistic and a parameter
are related.
Foundations (5)

Which of the following variables has the
greatest variation?
Variable
Tar cont
Nicotine
Carbon
Mean Median StDev
12.22 12.80 5.67
0.876 0.9000 0.3541
12.528 13.000 4.740
r,

2
r,
2
R
(1)
The correlation measures the ______
and ______ of the linear association
between two variables.
r,
2
R
(2)
Based on this plot of Nicotine vs. CO level and common
knowledge, do you feel that simple linear regression is a
sound choice of analysis in this setting? Explain.
Carbon monoxide content (mg)

2
r,
20
10
0
0
1
Nicotine content (mg)
2
r,

2
r,
2
R
(3)
In this study, the correlations between the
variables are:
Nicotine (x1) and CO (y): 0.977
Tar content (x2) and CO (y): 0.957
Nicotine (x1) and Tar content (x2): 0.926

Which variables would be helpful for
explaining CO levels? Explain any
concerns you might have about including
both predictors in a multiple regression
model?
r,

2
r,
2
R
(4)
If you find a very strong linear correlation
between two variables x and y, would you
claim that a causal relationship exists
between these variables? Explain.
r,

2
r,
2
R
(5)
Minitab reports both the R-square and the Rsquare (adjusted) values for models. Explain
why R-square (adjusted) is a better estimate
as compared to R-square.
Hypothesis Testing (1)

In a hypothesis test, if the p-value = .94 and
you have set alpha at .05, would you reject or
fail to reject the null hypothesis?
Hypothesis Testing (2)

If p < α, you would _____ H0.
Hypothesis Testing (3)

If H0 is true and we reject it, we have made a
___________________ error.
Hypothesis Testing (4)

In hypothesis testing, if I reject the null
hypothesis, can I accept that the
research hypothesis is correct? Explain.
Hypothesis Testing (5)

When I conduct significance tests for
the individual variables in a multiple
regression model, what am I testing?
Interpreting Regression Results (1)

Based on the sample, the simple linear
regression equation to estimate CO from
Nicotine Level is:
CO content = 1.66 + 12.4 (Nicotine
content)

Identify and interpret the slope in the context
of this problem.
Interpreting Regression Results (2)

have an R-square (adj.) value of 85.1%.
Explain what this means.
Interpreting Regression Results (3)

The F-statistic for the multiple regression
model for estimating CO Level from Nicotine
and Tar Content is F (2,22) = 124.11, p= 0.00.
If α= .01, what do you conclude?
Interpreting Regression Results (4)

If I have a simple linear regression
model and a multiple regression model
to predict the same dependent variable,
the Sum of Squares for the model
(SSM) increases with the multiple
regression model, but the Sum of
Squares Total (SST) is equal for both
models. Explain why.
Interpreting Regression Results (5)

Does each of the following predictor variables
contribute significantly to the model? (report the tvalue, df, and p-value tests of significance.)

CO content = 3.09 + 0.962 Tar - 2.65 Nicotine
Predictor
Constant
Tar cont
Nicotine
Coef
3.0896
0.9625
-2.646
SE Coef
0.8438
0.2367
3.787
T
P
3.66 0.001
4.07 0.001
-0.70 0.492