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 bivar data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of sixteen randomly selected days during the past year are given below. These data are plotted in scatter plot in Figure 1. Also given is the product of the temperature and the coffee sales for each of the sixteen days. (These products, written in the column labelled "xy", may aid in calculations.) Temperature, x Coffee sales, y (in dollars) 1969.0 146,099.8 1930.9 115,081.64 1963.7 139,815.44 2252.1 114,631.89 1744.4 117,223.68 1565.8 127,142.96 1970.5 75,273.1 2019.0 94,489.2 2116.3 99,889.36 1627.9 89,534.5 2247.6 89,229.72 1770.8 82,342.2 1625.8 118,520.82 1824.2 115,654.28 1544.2 1800.0 (in degrees Fahrenheit) 74.2 59.6 71.2 50.9 67.2 81.2 38.2 46.8 47.2 55.0 39.7 46.5 72.9 63.4 76.0 53.0 Send data to calc... ✓ xy 117,359.2 95,400 Send data to Excel X S 2400+ 2200- ↑y 2000- 1800- Coffee sales (in dollars) 1600 1400- 1200- Figure 1 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.) 40 50 60 70 80 90 Temperature (in degrees Fahrenheit)
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 bivar data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of sixteen randomly selected days during the past year are given below. These data are plotted in scatter plot in Figure 1. Also given is the product of the temperature and the coffee sales for each of the sixteen days. (These products, written in the column labelled "xy", may aid in calculations.) Temperature, x Coffee sales, y (in dollars) 1969.0 146,099.8 1930.9 115,081.64 1963.7 139,815.44 2252.1 114,631.89 1744.4 117,223.68 1565.8 127,142.96 1970.5 75,273.1 2019.0 94,489.2 2116.3 99,889.36 1627.9 89,534.5 2247.6 89,229.72 1770.8 82,342.2 1625.8 118,520.82 1824.2 115,654.28 1544.2 1800.0 (in degrees Fahrenheit) 74.2 59.6 71.2 50.9 67.2 81.2 38.2 46.8 47.2 55.0 39.7 46.5 72.9 63.4 76.0 53.0 Send data to calc... ✓ xy 117,359.2 95,400 Send data to Excel X S 2400+ 2200- ↑y 2000- 1800- Coffee sales (in dollars) 1600 1400- 1200- Figure 1 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.) 40 50 60 70 80 90 Temperature (in degrees Fahrenheit)
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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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 sixteen randomly selected days during the past year are given below. These data are plotted in the
scatter plot in Figure 1. Also given is the product of the temperature and the coffee sales for each of the sixteen days.
(These products, written in the column labelled "xy", may aid in calculations.)
Temperature,
x
Coffee
sales, y
(in
dollars)
1969.0
146,099.8
1930.9
115,081.64
1963.7 139,815.44
2252.1 114,631.89
1744.4 117,223.68
1565.8 127,142.96
1970.5
75,273.1
2019.0
94,489.2
2116.3
99,889.36
1627.9 89,534.5
2247.6
89,229.72
1770.8
82,342.2
1625.8
1824.2
1544.2
1800.0
(in degrees
Fahrenheit)
74.2
59.6
71.2
50.9
67.2
81.2
38.2
46.8
47.2
55.0
39.7
46.5
72.9
63.4
76.0
53.0
Send data to calc... v
xy
118,520.82
115,654.28
117,359.2
95,400
Send data to Excel
X
Coffee sales
(in dollars)
S
↑y
2400+
2200+
2000
1800.
1600-
1400+
1200-
Figure 1
What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four
decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)
40 50 60 70 80 90
Temperature
(in degrees Fahrenheit)
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