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BUSI 405 Quiz 3 Multiple Regression Causal Models solutions complete answers

BUSI 405 Quiz 3 Multiple Regression Causal Models solutions complete answers 

 

Which of the following is not a method for estimating data with trend?

 

Serial correlation violates which classical assumption?

 

Stock price data show periods of relatively calm interrupted by periods of enhanced price volatility. This suggests stock price data are

 

In a regression of sales on income and seasonal dummy variables for a quarterly time series, a negative sign of the quarter 3 dummy variable means

 

If the residuals in a regression equation are positively autocorrelated, which of the following is not a problem when the least squares procedure is used?

 

Personnel Test

 

The personnel department of a large manufacturing firm selected a random sample of 23 workers. The workers were interviewed and given several tests. On the basis of the test results, the following variables were investigated: X2 = manual dexterity score, X3 = mental aptitude score, and X4 = personnel assessment score.

 

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results:

 

y
=
−212
 
+
1.90X2
 
+
2.00X3
 
+
0.25X4
 
Adjusted R2
=
0.75.
 
 
 
 
 
(0.50)
 
 
(0.060)
 
 
(0.20)
 
 
 
 
 

Note: The numbers shown in parentheses below the coefficients are the standard errors of the coefficients.

 

The quantities in parentheses are the standard errors of the regression coefficients. The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

 

What is the correct estimate for the number of units of work completed by a worker with a manual dexterity score of 100, a mental aptitude score of 80 and a personnel assessment score of 10? Use the regression estimated, as given, to make this calculation.

 

Autocorrelation in a regression model occurs when there is some correlation

 

Lackland

Lackland Ski Resort uses multiple regression to forecast ski lift revenues for the next week based on the forecasted number of days with temperatures above 10 degrees and predicted number of inches of snow. The following function has been developed:

Sales = 10,902 255 (number days predicted above 10 degrees) 300 (number of inches of snow predicted)

Other information generated from the analysis include

Adjusted R2 = 0.6789

Standard Error of the Estimate (SEE) = 1,879

F-statistic = 6.279 with a significance of 0.049

Which of the following represents an accurate interpretation of the results of Lackland’s regression analysis?

 

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. The builder randomly selected 50 families and ran a multiple regression. The regression statistics are below:

 

Regression Statistics

 

 
 
 
R Square
 
0.748
Adjusted R Square
 
0.726
Standard Error
 
5.195
Observations
 
50
 
 

ANOVA Table
 
df
SS
MS
F
Sig. F
Regression
 
 
3605.7736
 
 
901.4434
 
 
 
 
 
0.0001
 
Error
 
 
1214.2264
 
 
29.9892
 
 
 
 
 
 
 
Total
49
 
4820.0000
 
 
 
 
 
 
 
 
 
 
 
 

 
Coefficient
Std. Error
T-test
P-Value
Intercept
 
 
−1.6335
 
 
5.8078
 
 
 
−0.281
 
 
0.7798
 
Income
 
 
0.4485
 
 
0.1137
 
 
 
3.9545
 
 
0.0003
 
Size
 
 
4.2615
 
 
0.8062
 
 
 
5.286
 
 
0.0001
 
School
 
 
−0.6517
 
 
0.4319
 
 
 
−1.509
 
 
0.1383
 
 
 

Dependent variable is House.

 

Referring to the Real Estate Builder regression results, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, she obtained an Adjusted R Squared value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

 

Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

 

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

 

 

 

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

 

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation
SS
df
MS
SEE
Regression
 
1,834,180.23
 
 
5
 
 
366,836.05
 
 
 
 
Error
 
494,506.47
 
 
34
 
 
14,544.31
 
 
120.60
 
Total
 
2,328,686.70
 
 
39
 
 
 
 
 
 
 
 
 

Audit Trail — Coefficient Table (Multiple Regression Selected)
 
Series Description
Included in Model
Coefficient
Standard Error
T-test
P-value
F-test
Elasticity
Overall F-test
DCS
 
Dependent
 
 
3,266.66
 
 
288.10
 
 
11.34
 
 
0.00
 
 
128.56
 
 
 
 
 
25.22
 
DCSP
 
Yes
 
 
−0.10
 
 
0.01
 
 
−7.18
 
 
0.00
 
 
51.50
 
 
−0.76
 
 
 
 
PR
 
Yes
 
 
−21.17
 
 
13.77
 
 
−1.54
 
 
0.13
 
 
2.36
 
 
−0.11
 
 
 
 
Q2
 
Yes
 
 
292.88
 
 
54.02
 
 
5.42
 
 
0.00
 
 
29.39
 
 
0.04
 
 
 
 
Q3
 
Yes
 
 
149.07
 
 
54.11
 
 
2.76
 
 
0.01
 
 
7.59
 
 
0.02
 
 
 
 
Q4
 
Yes
 
 
−60.25
 
 
54.22
 
 
−1.11
 
 
0.27
 
 
1.23
 
 
−0.01
 
 
 
 
 
 

Audit Trail - Statistics
 
 
 
 
 
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
492.41
 
Durbin Watson
1.62
 
BIC
494.10
 
Mean
1,802.86
 
Mean Absolute Percentage Error (MAPE)
5.30
%
Standard Deviation
244.36
 
R-Square
78.76
%
Max
2,272.60
 
Adjusted R-Square
75.64
%
Min
1,421.30
 
Root Mean Square Error
111.19
 
Range
851.30
 
 
 

For the domestic car sales regression, the multiple coefficient of determination shows that

 

Using the significance levels reported by Forecast XTM, at what level can we reject a one-sided null relating to a slope coefficient's statistical significance such that we are 95% confident?

 

A multiple regression model using 200 data points (with three independent variables) has how many degrees of freedom for testing the statistical significance of individual slope coefficients?

 

A residual is

 

In table 4.1 from the text, four different data sets are displayed along with the regressions associated with each data set. What point was being made in the text?

 

Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

 

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

 

 

 

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

 

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation
SS
df
MS
SEE
Regression
 
1,834,180.23
 
 
5
 
 
366,836.05
 
 
 
 
Error
 
494,506.47
 
 
34
 
 
14,544.31
 
 
120.60
 
Total
 
2,328,686.70
 
 
39
 
 
 
 
 
 
 
 
 

Audit Trail — Coefficient Table (Multiple Regression Selected)
 
Series Description
Included in Model
Coefficient
Standard Error
T-test
P-value
F-test
Elasticity
Overall F-test
DCS
 
Dependent
 
 
3,266.66
 
 
288.10
 
 
11.34
 
 
0.00
 
 
128.56
 
 
 
 
 
25.22
 
DCSP
 
Yes
 
 
−0.10
 
 
0.01
 
 
−7.18
 
 
0.00
 
 
51.50
 
 
−0.76
 
 
 
 
PR
 
Yes
 
 
−21.17
 
 
13.77
 
 
−1.54
 
 
0.13
 
 
2.36
 
 
−0.11
 
 
 
 
Q2
 
Yes
 
 
292.88
 
 
54.02
 
 
5.42
 
 
0.00
 
 
29.39
 
 
0.04
 
 
 
 
Q3
 
Yes
 
 
149.07
 
 
54.11
 
 
2.76
 
 
0.01
 
 
7.59
 
 
0.02
 
 
 
 
Q4
 
Yes
 
 
−60.25
 
 
54.22
 
 
−1.11
 
 
0.27
 
 
1.23
 
 
−0.01
 
 
 
 
 
 

Audit Trail - Statistics
 
 
 
 
 
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
492.41
 
Durbin Watson
1.62
 
BIC
494.10
 
Mean
1,802.86
 
Mean Absolute Percentage Error (MAPE)
5.30
%
Standard Deviation
244.36
 
R-Square
78.76
%
Max
2,272.60
 
Adjusted R-Square
75.64
%
Min
1,421.30
 
Root Mean Square Error
111.19
 
Range
851.30
 
 
 

For the domestic car sales regression above, the "third quick check" shows what (i.e., accuracy)?

 

In a multiple regression analysis involving two independent variables, if b1 is computed to be + 2.0, it means that

 

The autocorrelation parameter defined as 

ρ = cov(∈t,∈t−1)var(∈t) 

is used to measure

 

In using quarterly time series data, which quarter can serve as the base period for interpretation of dummy variables?

 

The following output resulted from a regression model where SAGap is seasonally adjusted Gap sales and dpi is disposable income per capita.

 

 

 

Audit Trail -- Coefficient Table (Mulitple Regression Selected)
Series Description
Included in Model 
Coefficient 
Standard Error 
T-test 
P-value 
F-test 
Elasticity 
SAGAP
 
Dependent
 
-
2,867,564.78
 
 
140,536.33
 
-
20.40
 
 
0.00
 
 
416.34
 
 
 
 
dpi
 
Yes
 
 
809.79
 
 
25.04
 
 
32.33
 
 
0.00
 
 
1,045.55
 
 
2.91
 
 
 

Audit Trail -- Correlation Coefficient Table
Series Description
Included in Model
SAGap
dpi
SAGap
 
Dependent
 
 
1.00
 
 
0.97
 
dpi
 
Yes
 
 
0.97
 
 
1.00
 
 
  

Audit Trail - Statistics
 
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
2,135.23
 
Durbin Watson(4)
0.43
 
BIC
2,137.56
 
Mean
1,501,041.15
 
Mean Absolute Percentage Error (MAPE)
34.60
%
Standard Deviation
1,303,264.45
 
R-Square
94.59
%
Max
4,253,174.95
 
Adjusted R-Square
94.51
%
Min
123,121.77
 
Mean Square Error
90,711,613,878.48
 
Range
4,130,053.18
 
Root Mean Square Error
301,183.69
 
Root Mean Square
1,294,661.95
 
Theil
6.23
 
Ljng-Box
347.40
 
 
 

Bottled Water

 

 

 

Shown above is the demand for bottled water in thousands of Gallons for 110 consecutive weeks. From weeks 75 through 84, there was a severe flood in the area. Shown below are two regression results using this data. The “Week” variable is an index of weeks from 1 through 109. The “Intervention” variable is a dummy variable equaling one during the intervention and zero otherwise.

 

Regression #1

 

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation
SS
df
MS
SEE
Regression
 
33,763.50
 
 
1
 
 
33,763.50
 
 
 
 
Error
 
6,697.97
 
 
108
 
 
62.02
 
 
7.88
 
Total
 
40,461.47
 
 
109
 
 
 
 
 
 
 
 
 

Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description
Included in Model
Coefficient
Standard Error
T-test
P-value
 
Elasticity
 
Overall F-test
Week
 
Yes
 
 
0.55
 
 
0.02
 
 
23.33
 
 
0.00
 
 
 
0.25
 
 
 
 
 
Demand
 
Dependent
 
 
94.28
 
 
1.51
 
 
62.35
 
 
0.00
 
 
 
 
 
 
 
544.41
 
 
 

Audit Trail — Correlation Coefficient Table
Series Description
Included in Model
Week
Demand
Week
 
Yes
 
 
1.00
 
 
0.91
 
Demand
 
Dependent
 
 
0.91
 
 
1.00
 
 
 

Audit Trail - Statistics
 
 
 
 
 
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
766.17
 
Durbin Watson
0.60
 
BIC
768.87
 
Mean
124.90
 
Mean Absolute Percentage Error (MAPE)
4.00
%
Standard Deviation
19.27
 
R-Square
83.45
%
Max
167.08
 
Adjusted R-Square
83.29
%
Min
89.55
 
Mean Square Error
60.89
 
Range
77.54
 
Root Mean Square Error
7.80
 
 
 
 
 
 

Method Statistics
Value
Method Selected
Multiple Regression
 
 

Regression #2

 

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation
SS
df
MS
SEE
Regression
 
38,993.33
 
 
2
 
 
19,496.66
 
 
 
 
Error
 
1.468.14
 
 
107
 
 
13.72
 
 
3.70
 
Total
 
40,461.47
 
 
109
 
 
 
 
 
 
 
 
 

Audit Trail — Coefficient Table (Multiple Regression Selected)
 
Series Description
Included in Model
Coefficient
Standard Error
T-test
P-value
 
Elasticity
Overall F-test
Week
 
Yes
 
 
0.50
 
 
0.01
 
 
43.50
 
 
0.00
 
 
 
0.22
 
 
 
 
Demand
 
Dependent
 
 
95.00
 
 
0.71
 
 
133.39
 
 
0.00
 
 
 
 
 
 
1,420.94
 
Intervention
 
Yes
 
 
24.70
 
 
1.27
 
 
19.52
 
 
0.00
 
 
 
0.22
 
 
 
 
 
 

Audit Trail — Correlation Coefficient Table
 
Series Description
Included in Model
Week
Demand
Intervention
Week
 
Yes
 
 
1.00
 
 
0.91
 
 
0.24
 
Demand
 
Dependent
 
 
0.91
 
 
1.00
 
 
0.57
 
Intervention
 
Yes
 
 
0.24
 
 
0.57
 
 
1.00
 
 
 

Audit Trail - Statistics
 
 
 
 
 
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
599.21
 
Durbin Watson
1.84
 
BIC
601.91
 
Mean
124.90
 
Mean Absolute Percentage Error (MAPE)
2.47
%
Standard Deviation
19.27
 
R-Square
96.37
%
Max
167.08
 
Adjusted R-Square
96.30
%
Min
89.55
 
Mean Square Error
13.35
 
Range
77.54
 
Root Mean Square Error
3.65
 
 
 
 
 
 

Method Statistics
Value
Method Selected
Multiple Regression
 
 

Examine the Akaike Information Criterion for both Regression #1 and Regression #2 above.

 

The inclusion of seasonal dummy variables to a multiple regression model may help eliminate

 

Cross-sectional regression models linking personal disposable income to consumption expenditure are likely to be hampered by

 

First-differencing the data is a way to

 

Which of the following is not correct about causal regression analysis of the form Y = f(X)?

 

Perfect multicollinearity is the

 

Which of the following is not recommended in selecting the correct set of independent variables for multiple regression?

 

ForecastX Regressions

 

Exhibit #1

 

Audit Trail — Coefficient Table (Multiple Regression Selected)
 
 
Series
Description
Included in Model
 
Coefficient
 
Standard Error
 
T-test
 
P-value
 
F-test
 
Elasticity
 
Overall F-test
SALES
 
Dependent
 
 
 
−51.24
 
 
 
54.32
 
 
 
−0.94
 
 
 
0.36
 
 
 
0.89
 
 
 
 
 
 
 
8.98
 
PRICE
 
Yes
 
 
 
30.92
 
 
 
10.32
 
 
 
3.00
 
 
 
0.01
 
 
 
8.98
 
 
 
1.46
 
 
 
 
 
 
 

Audit Trail — Correlation Coefficient Table
Series Description
Included in Model
SALES
PRICE
SALES
 
Dependent
 
 
1.00
 
 
0.63
 
PRICE
 
Yes
 
 
0.63
 
 
1.00
 
 
 

Audit Trail - Statistics
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
130.02
 
Durbin Watson(1)
0.34
 
BIC
130.80
 
Mean
111.19
 
Mean Absolute Percentage Error (MAPE)
10.67
%
Standard Deviation
17.49
 
R-Square
39.07
%
Ljung-Box
39.71
 
Adjusted R-Square
34.72
%
 
 
 
Root Mean Square Error
13.22
 
 
 
 
 
 

Exhibit #2

 

Audit Trail — Coefficient Table (Multiple Regression Selected)
 
Series
Description
Included in Model
Coefficient
Standard Error
T-test
P-value
F-test
Elasticity
Overall F-test
SALES
 
Dependent
 
 
123.47
 
 
19.40
 
 
6.36
 
 
0.00
 
 
40.51
 
 
 
 
 
154.86
 
PRICE
 
Yes
 
 
−24.84
 
 
4.95
 
 
−5.02
 
 
0.00
 
 
25.17
 
 
−1.17
 
 
 
 
INCOME
 
Yes
 
 
0.03
 
 
0.00
 
 
13.55
 
 
0.00
 
 
183.62
 
 
1.06
 
 
 
 
 
 

Audit Trail — Correlation Coefficient Table
 
Series Description
Included in Model
SALES
PRICE
INCOME
SALES
 
Dependent
 
 
1.00
 
 
0.63
 
 
0.94
 
PRICE
 
Yes
 
 
0.63
 
 
1.00
 
 
0.83
 
INCOME
 
Yes
 
 
0.94
 
 
0.83
 
 
1.00
 
 
 

Audit Trail - Statistics
Accuracy Measures
Value
 
Forecast Statistics
Value
 
AIC
86.56
 
Durbin Watson(1)
1.67
 
BIC
87.34
 
Mean
111.19
 
Mean Absolute Percentage Error (MAPE)
2.22
%
Standard Deviation
17.49
 
R-Square
95.97
%
Ljung-Box
15.22
 
Adjusted R-Square
95.35
%
 
 
 
Root Mean Square Error
3.40
 
 
 
 
 
 

Consider the two regressions shown above.

 

Regression model disturbances (forecast errors)

 

What is the approximate 95% prediction interval for the dependent variable when the independent variable value is 20, assuming the fitted regression line is: Y = 1.50 + 6.0(X). Assume the sample size is 20 and the standard error of the regression (SEE) is 1.2. You should use the "rule of thumb" used in class here.

 

When severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated?

 

 

If the linear assumption in regression is violated?

 

Which of the following is not an assumption of multiple regression models?

 

A regression of retail sales on disposable income and two interest rates, the prime rate and the short-term savings rate, is likely to have the problem of

 

Perfect multicollinearity is the

 

Dummy variables

 

Personnel Test

 

Note:  The next few questions utilize the following information:

 

The personnel department of a large manufacturing firm selected a random sample of 23 workers.  The workers were interviewed and given several tests.  On the basis of the test results, the following variables were investigated: X2 = manual dexterity score, X3 = mental aptitude score, and X4 = personnel assessment score.

 

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker.  Regression analysis yielded these results:

Y = -212 + 1.90X2 + 2.00X3 + 0.25X4,          R2 = .75.

(.050)      (.060)        (.20)

 

The quantities in parentheses are the standard errors of the regression coefficients.  The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

 

Which variables are making a significant contribution to the prediction of units of work completed at the .01 significance level (two tailed)?

 

Which of the following statements is the correct interpretation of the mental aptitude regression coefficient?

 

What percent of the variation of units of work completed can be explained by this model?

 

What is the correct estimate for the number of units of work completed by a worker with a manual dexterity score of 100, a mental aptitude score of 80 and a personnel assessment score of 10?

 

What is the table t value to test whether a regression coefficient is statistically significant at the .05 level (one tailed) for this problem?

 

Graphically, a multiple regression model with two independent variables looks like a

 

A multiple regression model using 200 data points (with three independent variables) has how many degrees of freedom for testing the statistical significance of individual slope coefficients?

 

Using the significance levels reported by ForecastXTM, at what level can we reject a one-sided null relating to a slope coefficient’s statistical significance such that we are 95% confident?

 

What action may reduce multicollinearity when two independent variables have a common trend?

 

Which of the following is not recommended in selecting the correct set of independent variables for multiple regression?

 

How are the AIC and BIC model selection criteria used in the model selection process for multiple regression?

 

Which of the following is not correct about near multicollinearity?

 

Estimated Demand Function

 

The following is an estimated demand function:

 

Q  =  875  + 6 XA  +  15 Y –  5 P

(125)       (2)         (4)     (-1.2)

 

Where Q is quantity sold, XA is advertising expenditure (in thousands of dollars), Y is income (in thousands of dollars), and P is the good’s price.  The standard errors for each estimate are in parentheses.  The equation has been estimated from 10 years of quarterly data.  The R2 was .92; the F-statistic was 57; the Standard Error of the Estimate (SEE) is 25.

 

According to the common 95 percent level of significance (estimated) for the regression above,

 

Suppose the values of the explanatory variables next period are: Advertising  =  $100,000; Income  =  $10,000; and Price  = $100.  Using the above fitted regression, what is the predicted value of sales?

 

For the above regression, an estimated 95 percent confidence interval around the sales prediction would be

 

When autocorrelation is present, which of the following is not a problem?

 

Which of the following “goodness-of-fit” measures should not be used in the context of multiple regression?

 

The F-statistic in the multiple regression model

 

A potential diagnosis and/or cure for the multicollinearity problem does not include

 

Forecasters who base model selection criteria on the maximization of R2 should

 

Multicollinearity in a regression model occurs when

 

Which statement is not correct?

 

When autocorrelation is present, which of the following is a problem?

 

The F-test in multiple regression

 

The F-statistic reported in standard multiple regression computer packages tests which hypothesis?

 

The Durbin-Watson statistic

 

Which of the following statements are true?

 

The inclusion of seasonal dummy variables to a multiple regression model may help eliminate

 

Consider the following group: R-squared, Adjusted R-squared, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC).  Which one doesn’t belong with the rest of the others?

 

Model A has an AIC number of  300 whereas model B has an AIC number of 400 (both models have the same dependent variable).  This suggests that which model is more correctly specified?

 

Which of the following is not correct?  Seasonality in a time series data set containing quarterly observations can be handled by

 

A company has computed a seasonal index for its quarterly sales.  Which of the following statements about the index is not correct?

 

How would you model the effect of rain on attendance to a soccer game?

 

Which of the following is probably not a potential cause of data seasonality?

 

Quarterly seasonal dummy variables take on values

 

Including male and female dummy variables in the same regression to represent sex will likely result in

 

In using quarterly time series data, which quarter can serve as the base period for interpretation of dummy variables?

 

In a regression of sales on income and seasonal dummy variables for a quarterly time series, a negative sign of the quarter 3 dummy variable means

 

Which of the following types of models cannot be satisfactorily estimated using ordinary least squares regression (with or without data transformations)?

 

Which of the following statements is not true?

 

Which of the following is not useful advice in using multiple regression to generate forecasts?

 

Large and complicated forecasting models

 

Domestic Car Sales

 

Consider the following multiple regression model of domestic car sales (DCS) where:

 

DCS = domestic car sales

DCSP= domestic car sales price (in dollars)

PR= prime rate as a percent (i.e., 10% would be entered as 10)

Q2= quarter 2 dummy variable

Q3= quarter 3 dummy variable

Q4= quarter 4 dummy variable

 

Does the regression pass the “first quick check (i.e., economic realism)?”

 

For the domestic car sales regression, which variable coefficients pass the “second quick check (i.e., statistical significance)?”

 

For the domestic car sales regression above, the “third quick check” shows what (i.e., accuracy)?

 

In the domestic car sales regression above, what evidence do you have of any pattern in the error terms?

 

For the domestic car sales regression above, assume that:

 

DCSP = $10,000

PR= 10 percent

and that it is the first quarter of the year.

 

What will DCS be predicted to be by the regression model?

 

For the domestic car sales regression above, assume that:

 

DCSP = $10,000

PR= 10 percent

and that it is the first quarter of the year.

 

What will be the approximate 95% confidence interval for the DCS prediction?

 

In the domestic car sales function there is evidence of seasonality. How does the regression model show this evidence?

 

For the domestic car sales regression the coefficient of determination shows that

 

The domestic car sales model

 

The AIC can be of help in model selection when choosing among

 

The Principle of Parsimony is given in the following statement:

 

The Akaike rule of thumb is

 

Use the Akaike criterion

 

ForecastX Regressions

 

Exhibit #1

 

 

Exhibit #2

 

 

Consider the two regressions presented above in answering the following questions.

 

In the simple regression above

 

Consider the two regressions shown above.

 

Consider the two regressions shown above. For the multiple regression above the Akaike Information Criterion indicates

 

Consider the two regressions shown above.

 

Bottled Water

 

Shown above is the demand for bottled water in thousands of Gallons for 110 consecutive weeks. From weeks 75 through 84 there was a severe flood in the area. Shown below are two regression results using this data.

 

Regression #1

  

Regression #2

  

Consider the two regressions shown above. Which of the following statements is true?

 

Examine the Akaike Information Criterion for both Regression #1 and Regression #2 above.

 

Consider the two regressions immediately above. The “Intervention” variable in Regression #2 represents the flood period by taking on a value of “1” when there is a flood during that week and a value of zero otherwise. How would you interpret the coefficient of the “Intervention” variable in Regression #2?

 

Consider Regression #2 immediately above. You should use the rule of thumb taught in class to answer this question. In order to create the approximate 95% confidence interval for an estimate of demand

 

Consider the two regression models immediately above. When comparing these two regressions with respect to accuracy

 

Consider the two regressions immediately above. In using the Akaike Information Criterion and the Bayesian Information Criterion “closeness” counts (as in the game of horseshoes). Using the rule of thumb we learned in class regarding the interpretation of the information criteria we could correctly say

 

The Akaike Information Criterion (AIC) may be used

  

Television Add Yields

 

Television add yields are sometimes measured in millions of retained impressions. The following two regressions model the effectiveness of adds for 21 consumer products. The data is from The Wall Street Journal, March 1, 1984.

 

The variables collected for each of the 21 products are:

SPENDING: TV advertising budget, ($ millions) MILIMP: Millions of retained impressions, MILIMP Sqrd: Millions of retained impressions squared.

  

A scatterplot of the data used appears below:

 

Regression #1

 

Regression #2

  

Regression #1 above

 

Regression #2 above for TV Add Yields

 

For the TV Add Yield regressions above

  

Education

 

A question of interest to many educators and college admissions officers is whether and to what extent high school students’ performance on standardized tests can forecast their performance in college. That is, does how well a student do on a test before entering college bear any relationship to his/her performance in college.

Jeffrey Wooldridge used data collected by Christopher Lemmon at Michigan State University to examine this question. The data contain information about students’ final GPA for all years of college, their performance on the ACT (a standardized test commonly used for college admissions), and their high school GPA (labeled hsGPA below). They estimated models to examine the links between GPA in college and these two separate pre-college measures.

Estimating their regression equation in a statistical software package yielded the following results:

Note: “_cons” is the constant term in the regression.

The dependent variable is “college GPA” shown as colGPA above.

 

According to this regression, the most predictive variable for forecasting college GPA was

 

In the Education regression ACT is best described as a(n)

 

In the Education regression college GPA is best described as a(n)

 

The internal auditor of a bank has developed a multiple regression model which has been used for a number of years to forecast the amount of interest income from commercial loans. During the current year, the auditor applies the model and discovers that the adjusted R2 value has decreased dramatically, but otherwise the model seems to be working okay. Which of the following conclusions are justified by the change?

 

Lackland

 

Lackland Ski Resort uses multiple regression to forecast ski lift revenues for the next week based on the forecasted number of days with temperatures above 10 degrees and predicted number of inches of snow. The following function has been developed:

 

Sales = 10,902 + 255 (number days predicted above 10 degrees) +

300 (number of inches of snow predicted)

 

Other information generated from the analysis include

 

Adjusted R2  = .6789

Standard Error of the Estimate (SEE) = 1,879

F-statistic = 6.279 with a significance of .049

 

Which variable(s) in this function is (are) the dependent variable(s)?

 

Assume that the management predicts the number of days above 10 degrees for the next week to be 6 and the number of inches of snow to be 12. Calculate the predicted amount of revenue for the next week.

 

Which of the following represents an accurate interpretation of the results of Lackland’s regression analysis?

 

Assume that Lackland’s model predicts revenue for a week to be $13,400. Calculate the 95% confidence interval for the amount of revenue for the week. (The 95% confidence interval corresponds to the area representing 2.3436 deviations from the mean.)

 

The least squares procedure minimizes the sum of

 

A residual is

 

The condition expectation of a random variable

 

The Y-intercept of the simple regression model

 

The Y-intercept of a regression line is -14 and the slope is 3.5. Which of the following is not correct?

 

Income is used to predict savings. For the regression equation Y = 1,000 + .10X, which of the following is true?

 

The sign on the slope estimate in a regression problem

 

X-Y data have been collected in which X ranges between 50 and 100 and Y ranges between 1200 and 2000. It is not wise to use the resulting regression line equation to predict Y when X is equal to -10 because:

 

The following regression equation was estimated: Y = -2.0 + 4.6X. This indicates that

 

Which of the following is not a reason to employ simple linear regression to generate sales forecasts for a retail outlet store?

 

Sample regression model forecast errors are called

 

The regression slope term (b) in the simple bivariate regression model is

 

Regression model disturbances (forecast errors)

 

Testing for the statistical significance of the relationship between the dependent and independent variable in small samples

 

Serial correlation causes estimates of the

 

Two data sets that have the exact same estimated linear regression must be the same data.

 

Visual inspection of the data will help the forecaster identify

 

Which of the following is a tool used in model selection?

 

Which of the following is not a recommended step in preparing a forecast using the simple linear regression model?

 

Fit and accuracy

 

Which of the following is not a method for estimating data with trend?

 

The most common mathematical trend equation for a time series is called the least squares trend because it is the line which minimizes the sum of the

 

Consider the following model: Sales = a + b(TIME)2+ e.  The trend is modeled here as a

 

Seasonal indices of sales for the Black Lab Ski Resort are for 1.20 for January; and .80 for December. If December sales for 1998 were $5,000, a reasonable estimate of sales for January 1999 is:

 

The expected trend value of September sales for a firm is $900. Assuming a September seasonal index of .91, what would be the seasonally adjusted forecast for September?

 

Which of the following is not correct about causal regression analysis of the form Y = f(X)?

 

What is the lesson learned from William Stanley Jevons’ sunspot theory of the business cycle?

 

Consider the following model linking seasonally adjusted retail-store sales (RSSA) to disposable personal income (DPI):

 

RSSA  =  -1,813,520 + 127.429(DPI).

 

If the quarter four seasonal index is 1.07264 and DPI is 19,119.6, our forecast for quarter-four sales is:

 

Note:  The following seasonal index numbers for sales of Big Daddy Chocolates (BDC) are used to answer the next three questions.

 

Month                                     Seasonal Index

 

January                                            1.20

February                                           .90

March                                              1.00

April                                                1.08

May                                                 1.02

June                                                 1.10

July                                                  1.05

August                                              .90

September                                         .85

October                                            1.00

November                                        1.10

December                                         .80

 

Total annual sales for BDC in 2001 are forecasted at $120 million. Based on the seasonal indexes above, sales in the first three months of 2001 should be:

 

If December 2000 sales for BDC are 20 million, what is a reasonable estimate for sales in January of 2001?

 

If BDC sales in November of 2000 were 12 million dollars, November sales after adjustment for seasonal variation are:

 

Which of the following statements are true?

 

Which of the following is incorrect?

 

The serial correlation parameter is used to measure

 

Which of the following is not used to solve the problem of serial correlation?

 

If the residuals in a regression equation are positively autocorrelated, which of the following is not a problem when the least squares procedure is used?

 

Test the null hypothesis of zero serial correlation assuming a sample of 26 observations with two independent variables at the .05 significance level when the Durbin-Watson statistic is equal to 1.2. What is your conclusion?

 

When serial correlation is present, which of the following is not a problem?

 

When serial correlation is present in time series data, which underlying assumption is violated?

 

One method for solving the serial correlation problem is to take advantage of the correlation between adjacent observations. This method is called:

 

Which of the following is not an indicator of regression fit?

 

In a model linking personal expenditure on sports attire to personal income, the appropriate null to test the assertion that income is positively related to the sales of sports attire is:

 

Which null is appropriate for testing whether two mutual funds have differing rates of return?

 

Testing the null hypothesis that the slope coefficient is zero uses what sampling distribution for small sample sizes?

 

The significance level reported in standard statistical packages for the estimated slope coefficient relates to which hypothesis?

 

Which diagnostic test allows the researcher to claim that her model explains x-percent of the variation in the dependent variable?

 

Which of the following would indicate a perfect model fit?

 

Suppose the significance level for a slope estimate reported by the standard computer package is .08. If the null hypothesis is one-sided, we

 

Consider the following time trend regression model for explaining the behavior of disposable personal income (DPI): DPI = 17,000 + 41(TIME). If the regression standard error were 150, what is an approximate 95% prediction interval for quarter 3 sales?

 

Which of the following is not a consequence of serial correlation?

 

Serial correlation violates which classical assumption?

 

Which of the following does not become unreliable when serial correlation is present?

 

The sample variance for the ordinary least squares slope estimate in the simple bivariate regression model is estimated as follows:

 

Serial correlation in a regression model occurs when there is some correlation

 

Which of the following is not true concerning the consequences of serial correlation?

 

If R2is .95 in a simple regression model, it can be said that:

 

The serial correlation parameter defined as

 

Which of the following is not true regarding testing for serial correlation?

 

Serial correlation leads to or causes:

 

The Durbin-Watson statistic is based upon the pattern of the regression error terms.

 

In applying the Durbin-Watson test, the required inputs are

 

What possible decisions can be made using the Durbin-Watson test?

 

The best possible value of the Durbin-Watson statistic is:

 

Which of the following is most likely to cause serial correlation?

 

What is not likely to be a problem when applying ordinary least squares to cross-sectional data?

 

 

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