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Statistics for business and economics

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) The time-series model Xt = Tt × St × Ct × It is used for forecasting, where Tt, St, Ct, and It are respectively the trend, seasonal, cyclical, and irregular components of the time series, and Xt is the value of the time series at time t. The following estimates are obtained:  = 125,  = 0.92,  = 1.04, and

= 0.90. The model will produce a forecast of: 

Write the answer as following:

XXX.XX

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The table below is the quarterly data of the Shiller Real Home Price Index. To remove the seasonality a centered 4-point moving average is used.

 

Year

Real Home Price Index

1.1

106.5058955

1.2

109.3296707

1.3

101.2225795

1.4

100.0466076

2.1

105.8948393

2.2

103.8986687

2.3

103.9743275

2.4

114.7133093

3.1

114.199126

3.2

115.4621261

3.3

115.3166155

 

 What is the value of ?

Write the answer as following:

XXX.XX

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The table below is the quarterly data of the Shiller Real Home Price Index. To remove the seasonality a centered 4-point moving average is used.

 

Year

Real Home Price Index

1.1

106.5058955

1.2

109.3296707

1.3

101.2225795

1.4

100.0466076

2.1

105.8948393

2.2

103.8986687

2.3

103.9743275

2.4

114.7133093

3.1

114.199126

3.2

115.4621261

3.3

115.3166155

 

 What is the value of ?

Write the answer as following:

XXX.XX

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 A time series is a:

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In a multiple regression model, the following statistics are given: SSE = 100, R2 = 0.995, K = 5, and n = 15. Determine the multiple coefficient of determination adjusted for degrees of freedom.

Write the answer as following:

X.XXX

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In examining the determinants of income, data were collected regarding the characteristics of 45 adults, and the regression Y = β0 + β1X1 + β2X2 + β3X3 +ε was used, where Y is the annual income (in thousands of dollars), X1 is the person's age, X2 is his/her years of education, and X3 is a dummy variable = 1 if the adult is female.

  If you get

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 = 26.3 + 1.38x1 + 2.98x2 - 0.76x3 + 0.34(x2 x3) when you run the regression, how would you interpret the coefficient on his/her years of education?

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A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted multiple coefficient of determination. The adjusted multiple coefficient of determination is:

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A loan officer is interested in examining the determinants of the total dollar value of residential loans made during a month. She used Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε to model the relationship, where Y is the total dollar value of residential loans in a month (in millions of dollars), X1 is the number of loans, X2 is the interest rate, X3 is the dollar value of expenditures of the bank on advertising (in thousands of dollars), and X4 is a dummy variable equal to 1 if the observation is either June, July, or August.

  Suppose that she obtained

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 = 3.8 + 0.23x1 - 1.31x2 + 0.032x3 + 1.05x4 by using data from the past 24 months. How would we interpret the coefficient on x4?

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A loan officer is interested in examining the determinants of the total dollar value of residential loans made during a month. She used Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε to model the relationship, where Y is the total dollar value of residential loans in a month (in millions of dollars), X1 is the number of loans, X2 is the interest rate, X3 is the dollar value of expenditures of the bank on advertising (in thousands of dollars), and X4 is a dummy variable equal to 1 if the observation is either June, July, or August.

 Suppose that she obtained

Image failed to load
 = 3.8 + 0.23x1 - 1.31x2 + 0.032x3 + 1.05x4 - 0.22x3x4 by using data from the past 24 months. How would we interpret the coefficient of x3x4?

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In examining the determinants of income, data were collected regarding the characteristics of 45 adults, and the regression lnY = β0 + β1 lnX1 + β2 lnX2 + β3X3 + ε was used, where Y is the annual income (in thousands of dollars), X1 is the adult's age, X2 is his/her years of education, and X3 is a dummy

variable = 1 and is used if the adult is female. You run the regression and obtain the equation

ln
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 = 6.3 + 0.91 lnx1 + 1.3 ln x2 - 0.05x3.

 How would you interpret the coefficient on years of education?

 

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