Download File: ch12, Chapter 12: Simple Regression Analysis and Correlation

File: ch12, Chapter 12: Simple Regression Analysis and Correlation
True/False
1. If the coefficient of correlation between two numerical variables is -1, it means that the two
variables are not related.
Ans: False
Response: See section 12.1 Correlation
Difficulty: Medium
2. The process of constructing a mathematical model to predict or determine one variable by
another is called a regression analysis.
Ans: True
Response: See section 12.2 Introduction to Simple Regression Analysis
Difficulty: Easy
3. In simple regression the variable to be predicted is called the predictor variable.
Ans: False
Response: See section 12.2 Introduction to Simple Regression Analysis
Difficulty: Easy
4. In a simple regression analysis the predictor variable is called the independent or explanatory
variable.
Ans: True
Response: See section 12.2 Introduction to Simple Regression Analysis
Difficulty: Easy
5. Usually, the first step in regression analysis is to construct a scatter plot.
Ans: True
Response: See section 12.2 Introduction to Simple Regression Analysis
Difficulty: Medium
6. Data points that are apart from the rest of the points in a data set used in a regression analysis
are called extraordinary observations.
Ans: False
Response: See section 12.4 Residual Analysis
Difficulty: Medium
7. The sum of the residuals in any given regression analysis is always zero.
Ans: True
Response: See section 12.4 Residual Analysis
Difficulty: Medium
8. A linear regression model analysis assumes that the error terms are independent, normally
distributed and have the non-constant variances.
Ans: False
Response: See section 12.4 Residual Analysis
Difficulty: Hard
9. The numerical value of the coefficient of determination r2 varies from –1 to +1.
Ans: False
Response: See section 12.6 Coefficient of Determination
Difficulty: Medium
10. If a regression model has an r2 of 0.20, it means that about 20% of the variation in the
dependent variable is explained by the regression model.
Ans: True
Response: See section 12.6 Coefficient of Determination
Difficulty: Medium
11. In simple regression estimation, the confidence interval is always wider than the prediction
interval.
Ans: False
Response: See section 12.8 Estimation
Difficulty: Hard
Multiple Choice
12. A value of -1 for the coefficient of correlation between two variables means that the two
variables are ________________.
a) not related at all
b) very weakly related
c) weakly related
d) somewhat strongly related
e) perfectly related
Ans: e
Response: See section 12.1 Correlation
Difficulty: Hard
13. The following regression model was fitted to sample data with 12 observations:
ŷ = 30 + 4.50x. What is the change in the predicted value of y for a unit change in the value?
a) 30
b) 43.40
c) 4.50
d) 36
e) 57.00
Ans: c
Response: See section 12.3 Determining the Equation of the Regression Line
Difficulty: Medium
14. The following regression model was fitted to sample data with 12 observations:
ŷ = 30 + 4.50x. What is the predicted value of y for a given value of x = 6?
a) 30
b) 43.40
c) 4.50
d) 36
e) 57.00
Ans: e
Response: See section 12.4 Residual Analysis
Difficulty: Medium
15. The following regression model was fitted to sample data with 12 observations:
ŷ = 30 + 4.50x. What is the residual for an observation (x = 2, y = 40)?
a) 0
b) 1
c) 0.50
d) -0.50
e) -1
Ans: b
Response: See section 12.4 Residual Analysis
Difficulty: Medium
16. Which of the following is not an assumption of the regression model?
a) The model is linear
b) The error terms decrease as x values increase
c) The error terms are normally distributed
d) The error terms are independent
e) The error terms have constant variance
Ans: b
Response: See section 12.4 Residual Analysis
Difficulty: Medium
17. If the error variances of a regression model are not constant, it is called _________.
a) heteroscedasticity
b) homoscedasticity
c) nonlinearity
d) non independent error terms
e) multicollinearity
Ans: a
Response: See section 12.4 Residual Analysis
Difficulty: Medium
18. If the sum of squares of error for a simple regression model fitted for twelve pairs of
observations is 250, what is the standard error of the estimate for the model?
a) 4.00
b) 4.56
c) 4.77
d) 5.00
e) 5.07
Ans: d
Response: See section 12.5 Standard Error of the Estimate
Difficulty: Medium
19. If the standard error of the estimate for a regression model fitted to a large number of paired
observations is 1.75, approximately 68% of the residuals would lie within ______
a) −0.68 and +0.68
b) −0.95 and +0.95
c) −0.97 and +0.97
d) −1.75 and +1.75
e) −3.50 and +3.50
Ans: d
Response: See section 12.5 Standard Error of the Estimate
Difficulty: Medium
20. Some entries have been deleted from the following analysis of variance table that is part of
the computer output from a simple regression analysis of a data set containing 11 matched-pair
observations.
Source
Regression
Residual
Total
df
1
SS
11
19222.72
MS
9315.23
F
p-Value
0.017340862
Based on this output, what is the value of the mean square error?
a) 33.18
b) 990.749
c) 9315.23
d) 1100.83
e) 8.4619
Ans: b
Response: See section 12.7 Hypothesis Tests for the Slope of the Regression Model and Testing
the Overall Model
Difficulty: Hard
21. Some entries have been deleted from the following analysis of variance table that is part of
the computer output from a simple regression analysis of a data set containing 11 matched-pair
observations.
Source
Regression
Residual
Total
df
1
SS
11
19222.72
MS
9315.23
F
p-Value
0.01734
Based on this output, what is the value of the F statistic?
a) 33.18
b) 9907.49
c) 9315.23
d) 1100.83
e) 9.4022
Ans: e
Response: See section 12.7 Hypothesis Tests for the Slope of the Regression Model and Testing
the Overall Model
Difficulty: Hard
22. Some entries have been deleted from the following analysis of variance table that is part of
the computer output from a simple regression analysis of a data set containing 11 matched-pair
observations.
Source
Regression
Residual
Total
df
1
SS
9315.23
11
19222.72
MS
9315.23
F
Based on this output, what is the value of the standard error of estimate?
a) 31.48
b) 9907.49
c) 9315.23
d) 1100.83
e) 8.4619
Ans: a
Response: See section 12.5 Standard Error of the Estimate
Difficulty: Hard
p-Value
0.01734