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Hwk8SolnFinDrtBSp06 - Homework VIII Question 1 The...

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Homework VIII Question 1. The following question is designed to give you a better understanding of how regression works and how to use and interpret the regression output from Minitab. Imagine that you want to predict the number of walk-ins each night based on the number of canceled flights before 6:00PM at the local airport. Observation Number of Walk-ins Number of Canceled Flights Before 6:00PM 1 3 18 2 5 22 3 8 26 4 14 31 Please SHOW ALL of your work clearly and by hand. It is perfectly appropriate to use Minitab to check your answers. (STAT >REGRESSION > REGRESSION) a. Is this a regression problem or a correlation problem? Explain in two sentences or less. If a regression problem, explicitly define the predictor variable and the response variable. This is a regression because we expect the number of cancelled flights to have an influence upon the number of walk-ins (there’s a cause-effect outcome). The predictor variable is the number of cancelled flights and the response variable is the number of walk-ins. b. Compute and interpret the slope of this linear regression, using the formula = = - - - = 4 1 2 4 1 1 ) ( ) )( ( i i i i i x x y y x x b . (Or you may use the computational formula.) x-bar= 97/4=24.25 y-bar= 30/4=7.5 numerator: 78.5 denominator: 92.75 b1= 78.5/92.75=0.846 Obs Y X Yi-ybar Xi-xbar numerator denominator 1 3 18 -4.5 -6.25 28.125 39.0625 2 5 22 -2.5 -2.25 5.625 5.0625 3 8 26 0.5 1.75 0.875 3.0625 4 14 31 6.5 6.75 43.875 45.5625 SUM: 30 97 78.5 92.75 This tells us that as the number of cancelled flights before 6pm increase by 1, we would expect on average the number of walk-ins to increase by about 0.846.
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H ADM 201 Homework VIII Spring 2006 c. Compute and interpret the intercept of the estimated regression equation using the formula x b y b o 1 - = . Is the interpretation of this parameter realistic given the specifics of this problem? Why is this so? B0= 7.5-0.846*24.25=-13.02 This is not a realistic parameter because this would mean that we would actually have a negative number of walk ins if there were no cancelled flights. Obviously this doesn’t make sense. This occurs because we are attempting to extrapolate way further then the given data permits; the range of X values here is 18 to 31, and we are extrapolating back to x = 0. d. Using the estimated regression equation, compute the predicted values i y ˆ , and the residual, e i = y i - i y ˆ , for each i x in the data set. Obs x i walk-in (y i ) Yi-hat ei 1 18 3 2.2112 0.7888 2 22 5 5.5968 -0.5968 3 26 8 8.9824 -0.9824 4 31 14 13.2144 0.7856 e. Compute the estimate for the variance around the line, the MSE. Use this to compute and interpret the estimated standard deviation around the line.
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Hwk8SolnFinDrtBSp06 - Homework VIII Question 1 The...

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