Question 1

Which statement is incorrect?

Accepted Answer

A) Binary predictors shift the intercept of the fitted regression. 
B) If a qualitative variable has c categories, we would use only c - 1 binaries as predictors. 
C) A binary predictor has the same t test as any other predictor. 
D) If there is a binary predictor (X = 0, 1) in the model, the residuals may not sum to zero. 
A) Binary predictors shift the intercept of the fitted regression. 
B) If a qualitative variable has c categories, we would use only c - 1 binaries as predictors. 
C) A binary predictor has the same t test as any other predictor. 
D) If there is a binary predictor (X = 0, 1) in the model, the residuals may not sum to zero.

Question 2

The regression equation Salary = 28,000 + 2700 YearsExperience + 1900 YearsCollege describes employee salaries at Ramjac Corporation. The standard error is 2400. Mary has 10 years' experience and 4 years of college. Her salary is $58,350. What is Mary's standardized residual (approximately)?

Accepted Answer

A) -1.150 
B) +2.007 
C) -1.771 
D) +1.400 
A) -1.150 
B) +2.007 
C) -1.771 
D) +1.400

Question 3

A regression of Y using four independent variables X1, X2, X3, X4 could also have up to four nonlinear terms (X2) and six simple interaction terms (XjXk) if you have enough observations to justify them.

Accepted Answer

A) True 
 B)False

Question 4

Simple tests for nonlinearity in a regression model can be performed by

Accepted Answer

A) squaring the standard error. 
B) including squared predictors. 
C) deleting predictors one at a time. 
A) squaring the standard error. 
B) including squared predictors. 
C) deleting predictors one at a time.

Question 5

Using state data (n = 50) for the year 2000, a statistics student calculated a matrix of correlation coefficients for selected variables describing state averages on the two main scholastic aptitude tests (ACT and SAT). (a) In the spaces provided, write the two-tailed critical values of the correlation coefficient for α = .05 and α = .01 respectively. Show how you derived these critical values. (b) Mark with * all correlations that are significant at α = .05, and mark with ** those that are significant at α = .01. (c) Why might you expect a negative correlation between ACT% and SAT%? (d) Why might you expect a positive correlation between SATQ and SATV? Explain your reasoning. (e) Why is the matrix empty above the diagonal?
Correlation Matrix ( $n = 50$ states $)$

$\begin{array}{|c|c|c|c|c|}
\text { ACT } & A C T \% & \text { SAT\% } & \text { SATQ } & \text { SATV }\
\hline\text { ACT } & 1.000 & & & & \
\hline A C T \% &-0.232 & 1.000 & & & \
\hline \text { SAT\% } &0.139 & -0.966 & 1.000 & & \
\hline  \text { SATQ } & 0.213 & 0.818 & -0.856 & 1.000 & \
\hline \text { SATV }&0.092 & 0.862 & -0.889 & 0.963 & 1.000 \
\hline
\end{array}$

$A C T =$ average composite $A C T$ score
$A C T \%$ = percent of high school grads taking the ACT
SAT\% = percent of high school graduates taking SAT test
$S A T Q$ = average SAT quantitative test score
SATV = average SAT verbal test score
Critical value for $.05$
Critical value for $.01$

Accepted Answer

(a) As explained in Chapter 12, for d.f.

Question 6

Heteroscedasticity of residuals in regression suggests that there is:

Accepted Answer

A) nonconstant variation in the errors. 
B) multicollinearity among the predictors. 
C) non-normality in the errors. 
D) lack of independence in successive errors. 
A) nonconstant variation in the errors. 
B) multicollinearity among the predictors. 
C) non-normality in the errors. 
D) lack of independence in successive errors.

Question 7

A multiple regression with 60 observations should not have 13 predictors.

Accepted Answer

A) True 
 B)False

Question 8

In a multiple regression with k independent variables, the standard error is:

Accepted Answer

A) the sum of the squared residuals. 
B) the sum of the residuals. 
C) the sum of the residuals divided by n - k - 1. 
D) the square root of SSE divided by n - k - 1. 
A) the sum of the squared residuals. 
B) the sum of the residuals. 
C) the sum of the residuals divided by n - k - 1. 
D) the square root of SSE divided by n - k - 1.

Question 9

In a multiple regression with six predictors in a sample of 67 U.S. cities, what would be the critical value for an F-test of overall significance at α = .05?

Accepted Answer

A) 2.29 
B) 2.25 
C) 2.37 
D) 2.18 
A) 2.29 
B) 2.25 
C) 2.37 
D) 2.18

Question 10

The F-test for ANOVA in a regression model with 4 predictors and 47 observations would have how many degrees of freedom?

Accepted Answer

A) (3, 44) 
B) (4, 46) 
C) (4, 42) 
D) (3, 43) 
A) (3, 44) 
B) (4, 46) 
C) (4, 42) 
D) (3, 43)

Which statement is incorrect?

The regression equation Salary = 28,000 + 2700 YearsExperience + 1900 YearsCollege describes employee salaries at Ramjac Corporation. The standard error is 2400. Mary has 10 years' experience and 4 years of college. Her salary is $58,350. What is Mary's standardized residual (approximately)?

A regression of Y using four independent variables X₁, X₂, X₃, X₄ could also have up to four nonlinear terms (X²) and six simple interaction terms (X_jX_k) if you have enough observations to justify them.

Simple tests for nonlinearity in a regression model can be performed by

Heteroscedasticity of residuals in regression suggests that there is:

A multiple regression with 60 observations should not have 13 predictors.

In a multiple regression with k independent variables, the standard error is:

In a multiple regression with six predictors in a sample of 67 U.S. cities, what would be the critical value for an F-test of overall significance at α = .05?

The F-test for ANOVA in a regression model with 4 predictors and 47 observations would have how many degrees of freedom?

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 13: Multiple Regression

Which statement is incorrect?

The regression equation Salary = 28,000 + 2700 YearsExperience + 1900 YearsCollege describes employee salaries at Ramjac Corporation. The standard error is 2400. Mary has 10 years' experience and 4 years of college. Her salary is $58,350. What is Mary's standardized residual (approximately)?

A regression of Y using four independent variables X1, X2, X3, X4 could also have up to four nonlinear terms (X2) and six simple interaction terms (XjXk) if you have enough observations to justify them.

Simple tests for nonlinearity in a regression model can be performed by

Heteroscedasticity of residuals in regression suggests that there is:

A multiple regression with 60 observations should not have 13 predictors.

In a multiple regression with k independent variables, the standard error is:

In a multiple regression with six predictors in a sample of 67 U.S. cities, what would be the critical value for an F-test of overall significance at α = .05?

The F-test for ANOVA in a regression model with 4 predictors and 47 observations would have how many degrees of freedom?

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

A regression of Y using four independent variables X₁, X₂, X₃, X₄ could also have up to four nonlinear terms (X²) and six simple interaction terms (X_jX_k) if you have enough observations to justify them.