Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. Temperature, x (in degrees Fahrenheit) Coffee sales, y (in dollars) 67.3 1722.9 54.1 1596.0 2400- 76.0 1509.2 63.0 1842.6 2200 - 41.6 2296.7 2000- 46.9 2131.5 1800- 46.6 1805.0 45.6 1973.7 1600 83.4 1543.9 1400- 70.8 1952.9 76.2 1974.4 1200- 73.4 1638.1 58.3 1906.3 51.9 2245.9 Figure 1 38.8 1995.2 Send data to Excel Continue Submit Assignment O 2021 McGraw-Hill Education. All Rights Reserved. Terms of Use I Privacy Accessibility pe here to search 99+
Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1. Temperature, x (in degrees Fahrenheit) Coffee sales, y (in dollars) 67.3 1722.9 54.1 1596.0 2400- 76.0 1509.2 63.0 1842.6 2200 - 41.6 2296.7 2000- 46.9 2131.5 1800- 46.6 1805.0 45.6 1973.7 1600 83.4 1543.9 1400- 70.8 1952.9 76.2 1974.4 1200- 73.4 1638.1 58.3 1906.3 51.9 2245.9 Figure 1 38.8 1995.2 Send data to Excel Continue Submit Assignment O 2021 McGraw-Hill Education. All Rights Reserved. Terms of Use I Privacy Accessibility pe here to search 99+
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
Transcribed Image Text:Managers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict
a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum
temperature (denoted by x, in degrees Fahrenheit) for each of fifteen randomly selected days during the past year are given below. These data are plotted in the
scatter plot in Figure 1.
Temperature, x
(in degrees
Fahrenheit)
Coffee sales, y
(in dollars)
67.3
1722.9
54.1
1596.0
2400-
76.0
1509.2
63.0
1842.6
2200
41.6
2296.7
2000-
46.9
2131.5
1800-
46.6
1805.0
45.6
1973.7
1600--
83.4
1543.9
1400-
70.8
1952.9
76.2
1974.4
1200-
73.4
1638.1
58.3
1906.3
40
50
60
70
80
90
51.9
2245.9
Figure 1
38.8
1995.2
Send data to Excel
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ype here to search
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Transcribed Image Text:Send data to Excel
After deciding on the appropriateness of a linear model relating coffee sales and maximum temperature, the managers calculate the equation of the least-
squares regression line to be y = 2520.75-10.83x. This is the line shown in Figure 1.
Answer the following:
1. Fill in the blank: For these data, temperature values that are
greater than the mean of the temperature values tend to be paired
with coffee sales values that are
values.
the mean of the coffee sales
Choose one
2. According to the regression equation, for an increase of one degree
in temperature, there is a corresponding decrease of how many
dollars in coffee sales?
3. What was the observed coffee sales value (in dollars) when the
temperature was 73.4 degrees Fahrenheit?
4. From the regression equation, what is the predicted coffee sales
value (in dollars) when the temperature is 73.4 degrees Fahrenheit?
(Round your answer to at least one decimal place.)
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