Concept explainers
Management proposed the following regression model to predict sales at a fast-food outlet.
y = β0 + β1x1 + β2x2 + β3x3 + ε
where
x1 = number of competitors within one mile
x2 = population within one mile (1000s)
y = sales ($1000s)
The following estimated regression equation was developed after 20 outlets were surveyed.
ŷ = 10.1 − 4.2x1 + 6.8x2 + 15.3x3
- a. What is the expected amount of sales attributable to the drive-up window?
- b. Predict sales for a store with two competitors, a population of 8000 within one mile, and no drive-up window.
- c. Predict sales for a store with one competitor, a population of 3000 within one mile, and a drive-up window.
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Chapter 15 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
- Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forward
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