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Statistics for business and economics

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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
Image failed to load
 = 6.3 + 0.91 lnx1 + 1.3 ln x2 - 0.05x3.

 How would you interpret the coefficient on age?

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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
Image failed to load
 = 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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What would you forecast the occupancy rate to be this July when we expect 525,000 visitors?  We would anticipate the room rate to average $130 and consumer confidence to be 110

Prsent the answer as following:

XXX.XX%

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Interpret the estimate b1.

  For every one percent increase in the number of airline passengers, we would expect a 1.23 percent increase in the occupancy rate, assuming that all the other variables are fixed.

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The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month. Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers. He develops two models: Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε and Y = β0 + β1X1 + β2X2 + ε, where Y is the hotel occupancy rate (as a percentage), X1 is the total number of passengers arriving at the airport (measured in thousands), X2 is an average of local hotel room rates, X3 is the consumer confidence index, and X4 is a dummy variable = 1 during the months of June, July and August. He looks at data from the past 36 months and runs both of the regressions above. The results of these regressions are as follows:

Model 1: R2 = 0.67 and SSE = 576, Model 2: R2 = 0.61 and SSE = 733. Using the F- test on a subset of variables, test whether β3 = β4 = 0.

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Find a 95% confidence interval for βi. i=1,2,3

Present the answer as following:

(X.XX ± X.XXXX;X.XX ± X.XXXX;X.XX ± X.XXXX)

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As director of the local tourist board, you are interested in determining the factors that influence the hotel occupancy rate in your city each month. Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers. You develop the following model: Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε, where Y is the hotel occupancy rate, X1 is the total number of passengers arriving at the airport, X2 is a price index of local hotel room rates, X3 is the consumer confidence index, and X4 is a dummy variable = 1 during the months of June, July, and August. You look at data from the past 36 months and obtain the following results: y^ = 67.1 + 0.02x1 - 0.055x2 + 0.08x3 + 12.3x4, R2 = 0.67,  = 58.3,  = 0.008,  = 0.01,  = 0.06,  = 4.7, and SSE = 576.

 Calculate the total sum of squares.

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As director of the local tourist board, you are interested in determining the factors that influence the hotel occupancy rate in your city each month. Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers. You develop the following model: Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε, where Y is the hotel occupancy rate, X1 is the total number of passengers arriving at the airport, X2 is a price index of local hotel room rates, X3 is the consumer confidence index, and X4 is a dummy variable = 1 during the months of June, July, and August. You look at data from the past 36 months and obtain the following results: y^ = 67.1 + 0.02x1 - 0.055x2 + 0.08x3 + 12.3x4, R2 = 0.67,  = 58.3,  = 0.008,  = 0.01,  = 0.06,  = 4.7, and SSE = 576.

Calculate the regression sum of squares.

Give the answer as following

XXXX.XX

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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
Image failed to load
 = 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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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

Image failed to load
y^ = 26.3 + 1.38x1 + 2.98x2 - 0.76x3 when you run the regression, how would you interpret the coefficient on gender?

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