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Economy 3300

# Economy 3300 - 1 Review for in-class portion of Test#3(The...

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Review for in-class portion of Test #3 (The take-home problem will involve using Excel to perform a regression analysis.) 1 . Translate the team’s belief below into a model specification. Then indicate the signs of the model coefficients consistent with the team’s belief. An executive team for a chain of pharmacies gathered the following data on its existing pharmacies: Sales = dollar sales last quarter Pop = (estimated) number of people residing within ten miles of the pharmacy PCI = (estimated) per capita income of population within ten miles of the pharmacy Competitors = number of competitors within two miles of the pharmacy HighSchool = 1 if a high school is within one mile of the pharmacy, 0 otherwise The team believes that: Sales increases with PCI in a diminishing returns sense Sales are higher in a pharmacy with a high school within one mile than in a pharmacy without a high school within one mile Sales increases with Pop Sales decreases with the number of competitors 2 . The manager of a delivery-only pizza establishment wanted to assess the relationship between the time (in minutes) to travel to a customer’s residence and the distance (in miles) to the residence. For a random sample of 30 deliveries (of pizza to customer residences over the past month), the travel time and distance were recorded. The enclosed Excel sheet labeled Pizza Delivery scenario contains the results of a regression analysis on the sample data using a model specification of Time = β 0 + β 1 Distance + ε. Note : Using 2 decimal places is adequate. [source: Adapted from Weiers (2008)] (a) Graph (on the scatter diagram on the Excel sheet) the sample regression equation/line, being sure to specify (on or near the scatter diagram) two of the points on the line. (b) Based on the residual plot: Does the linearity assumption appear met? Does the equal variances assumption appear met? Does the normality assumption appear met? Assume henceforth that all model assumptions are adequately met. (c) Use the p-value approach to hypothesis testing to test H 0 : β 1 = 0 (d) Predict the time to travel to a residence 4.5 miles from the establishment. (e) Interpret the standard error of the estimate. (f) Interpret 1.68, the sample regression coefficient of Distance. (g) Suggest a variable besides Distance that could assist in predicting delivery time. (h) If the variable you suggested in (g) does indeed assist in predicting delivery time when used along with distance, what would you expect to happen to R 2 and what would you expect to happen to the standard error of the estimate if you gathered data on that variable and then re-ran the regression, this time regressing Time on Distance and that variable? 3 . A realty that sells homes along the east coast of the United States hopes to develop some guidelines regarding heating costs for single family homes. For a random sample of 20 homes along the east coast, the company determined: Cost = the heating cost (in \$) last January; Temperature = the mean outside temperature (in degrees Fahrenheit) last January; and Insulation = the number of inches of insulation in the attic.

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