Unformatted text preview: c: Time series regression 11632 Chapter 01  An Introduction to Business Statistics 108. Consider the following set of quarterly sales data given in thousands of dollars. The following dummy variable model that incorporates a linear trend and constant seasonal
variation was used: y (t) = B0 + B1t + BQ1(Q1) + BQ2(Q2) + BQ3(Q3) + Et
In this model there are 3 binary seasonal variables (Q1, Q2, and Q3).
Where
Qi is a binary (0, 1) variable defined as:
Qi = 1, if the time series data is associated with quarter i;
Qi = 0, if the time series data is not associated with quarter i.
The results associated with this data and model are given in the following MINITAB
computer output.
The regression equation is
Sales = 2442 + 6.2 Time  693 Q1  1499 Q2 + 153 Q3 Provide a managerial interpretation of the regression coefficient for the variable "time."
It is estimated that quarterly increase in sales is $6,200. AACSB: Analytic
Bloom's: Evaluation
Difficulty: Medium
Learning Objective: 2
Topic: Time series regression 11633 Chapter 01  An Introduction to Business Statistics 109. Consider the following set of quarterly sales data given in thousands of dollars. The following dummy variable model that incorporates a linear trend and constant seasonal
variation was used: y (t) = B0 + B1t + BQ1(Q1) + BQ2(Q2) + BQ3(Q3) + Et
In this model there are 3 binary seasonal variables (Q1, Q2, and Q3).
Where
Qi is a binary (0, 1) variable defined as:
Qi = 1, if the time series data is associated with quarter i;
Qi = 0, if the time series data is not associated with quarter i.
The results associated with this data and model are given in the following MINITAB
computer output.
The regression equation is
Sales = 2442 + 6.2 Time  693 Q1  1499 Q2 + 153 Q3 At α = .05, test the significance of the model.
Reject H0, the model is significant.
H0: β1 = βQ1 = βQ2 = βQ3 = 0 HA: At least one βj is not equal to zero.
Reject H0, if Fcalc > F4,7,.05
47.06 > 4.12, reject H0, the model is significant. 11634 Chapter 01  An Introduction to Business Statistics
AACSB: Analytic
Bloom's: Evaluation
Difficulty: Medium
Learning Objective: 2
Topic: Time series regression 110. The linear regression trend model was applied to a time series sales data based on the last
24 months' sales. The following partial computer output was obtained. Write the prediction equation.
y = 198.03 + 8.07t AACSB: Analytic
Bloom's: Comprehension
Difficulty: Easy
Learning Objective: 2
Topic: Time series regression 111. The linear regression trend model was applied to a time series sales data based on the last
24 months' sales. The following partial computer output was obtained. Test the significance of the time term at α = .05. State the critical t value and make your
decision using a twosided alternative.
t = 8.65, reject H0
t.025,22 = 2.074
8.65 > 2.074, reject H0.
It appears that time variable significantly affects the sales. AACSB: Analytic
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 2
Topic: Time series regression 11635 Chapter 01  An Introduction to Business Statistics 112. The linear regression trend model was applied to a time series sales data based on the last
24 months' sales. The following partial computer output was obtained. What is the predicted value of y when t = 25?
399.78 AACSB: Analytic
Bloom's: Application
Difficulty: Easy
Learning Objective: 2
Topic: Time series regression 113. Consider a time series with 15 quarterly sales observations. Using the quadratic trend
model the following partial computer output was obtained. Write the prediction equation.
y = 199.62 + 50.94t  .57t2 AACSB: Analytic
Bloom's: Comprehension
Difficulty: Easy
Learning Objective: 2
Topic: Time series regression 11636 Chapter 01  An Introduction to Business Statistics 114. Consider a time series with 15 quarterly sales observations. Using the quadratic trend
model the following partial computer output was obtained. State the twosided null and alternative hypothesis to test the significance of the t2 term.
H0: βT2 = 0 HA: βT2 ≠ 0 AACSB: Reflective Thinking
Bloom's: Knowledge
Difficulty: Medium
Learning Objective: 2
Topic: Time series regression 115. Consider a time series with 15 quarterly sales observations. Using the quadratic trend
model the following partial computer output was obtained. Test the significance of the t2 term at α = .05. State the critical t value (rejection point) and the
pvalue. Make your decision using a twosided null hypothesis.
t = 3.80, pvalue = .001, reject H0.
H0: βT2 = 0 HA: βT2 ≠ 0
t.25,13 = 2.16
Reject H0 if t > 2.16 or
Reject H0 if t < 2.16
Reject H0 if pvalue < .025
3.80 > 2.16. therefore reject H0 or
.001 < .025, therefore reject H0. AACSB: Analytic
Bloom's: Comprehension
Difficulty: Medium
Learning Objective: 2
Topic: Time series regression 11637 Chapter 01  An Introduction to Business Statistics 116. Consider a time series with 15 quarterly sales observations. Using the quadratic trend
model the fol...
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 Winter '14
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