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y ± (t) (s) (√1 + dv)
1.743 ± (2.160) (.4862) (√1 + .068975) → 0.657 to 2.829 AACSB: Analytic
Learning Objective: 5
Topic: Confidence & predication intervals 1-1299 Chapter 01 - An Introduction to Business Statistics
Essay Questions 149. Consider the following partial computer output from a simple linear regression analysis. S = 0.4862 R-Sq = 0.7286
Analysis of Variance Test to determine if there is a significant correlation between x and y. Use H0: ρ = 0 versus
Ha: ρ ≠ 0 by setting
= .01. Show the test statistic used in the decision.
A. -5.908, reject the null hypothesis
B. 5.908, reject the null hypothesis
C. 9.35, reject the null hypothesis
D. -2.977, reject the null hypothesis
Reject the null hypothesis, there is a significant correlation between x and y
r = -0.8536, then
t = (-0.8536) (√13)/(√1 - .7286) = -3.078/.5209 = -5.908 < -2.977, reject H0 AACSB: Analytic
Learning Objective: 6
Topic: Correlation Chapter 14
True / False Questions 1. Regression models that employ more than one independent variable are referred to as
multiple regression models.
True False 1-1300 Chapter 01 - An Introduction to Business Statistics 2. The error term in the regression model describes the effects of all factors other than the
independent variables on y (response variable).
True False 3. In a regression model, at any given combination of values of the independent variables, the
population of potential error terms is assumed to have an F-distribution.
True False 4. In a regression model, a value of the error term depends upon other values of the error
True False 5. A t-test is used in testing the significance of an individual independent variable.
True False 6. Due to the fact that multiple regression models consist of multiple independent variables,
residual analysis cannot be performed.
True False 1-1301 Chapter 01 - An Introduction to Business Statistics 7. When the F test is used to test the overall significance of a multiple regression model, if the
null hypothesis is rejected, it can be concluded that all of the independent variables x1, x2,
…xk are significantly related to the dependent variable y.
True False 8. For the same point estimate of the dependent variable and the same level of significance,
the confidence interval is always wider than the corresponding prediction interval.
True False 9. An application of the multiple regression model generated the following results involving
the F test of the overall regression model: p - value = .0012, R2 = .67 and s = .076. Thus, the
null hypothesis, which states that none of the independent variables are significantly related to
the dependent variable, should be rejected at the .05 level of significance.
True False 10. The multiple correlation coefficient can assume any value between zero and 1, inclusive.
True False 11. Testing the contribution of individual independent variables with t-tests is performed prior
to the F-test for the model in multiple regression analysis.
True False 12. The normal plot is a residual plot that checks the normality assumption.
True False 13. The assumption of independent error terms in regression analysis is often violated when
using time series data.
True False 1-1302 Chapter 01 - An Introduction to Business Statistics 14. In a multiple regression analysis, if the normal probability plot exhibits approximately a
straight line, then it can be concluded that the assumption of normality is not violated.
True False 15. Completely randomized analysis of variance models (one-way ANOVA) can always be
converted to a multiple regression models with dummy independent variables.
True False 16. If we are predicting y when the values of the independent variables are x01, x02, ….,x0k,
the farther the values of x01, x02,….,x0kare from the center of the experimental region, the
smaller the distance value and the more precise the associated confidence and prediction
True False Multiple Choice Questions 17. When using a multiple regression model, we assume that error terms (residuals) are
distributed according to a(n) ________________ distribution.
D. Poisson 18. The multiple coefficient of determination is the _______ divided by the total variation
A. Unexplained variation
C. Explained variation
D. Distance value
E. Leverage value 1-1303 Chapter 01 - An Introduction to Business Statistics 19. Which is not an assumption of a multiple regression model?
A. Positive autocorrelation of error terms
B. Normality of error terms
C. Independence of error terms
D. Constant variation of error terms 20. The range of feasible values for the multiple coefficient of determination is from:
A. 0 to
B. -1 to 0
C. -1 to 1
D. 0 to 1
E. to 0 21. The range of feasible values for the multiple coefficient of correlation is from:
A. 0 to
B. -1 to 0
C. -1 to 1
D. 0 to 1
E. to 0 22. For a given mult...
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