An electric utility wishes to examine the relationship between temperature and electricity use in its service region during the summer months. The bivariate data below give the maximum temperature (denoted by x, in degrees Fahrenheit) and the electricity use (denoted b y, in thousands of kilowatt hours) for a random sample of sixteen summer days. The data are shown in the Figure 1 scatter plot. Also given are the products of the temperature values and values for electricity use for each of the sixteen days. (These products, written in the column labelled "xy," may aid in calculations.) ху, Temperature, x Electricity use, y (in degrees Fahrenheit) (in thousands of kilowatt hours) ху 82.2 254.3 20903.46 88.8 309.3 27465.84 400- 81.0 298.2 24154.2 71.9 297.4 21383.06 375- 83.4 366.5 30566.1 350- 95.4 329.0 31386.6 325- 82.8 315.0 26082 300- XX 73.1 297.7 21761.87 275- 91.7 323.7 29683.29 91.4 343.3 31377.62 250 98.4 385.7 37952.88 225- 77.8 292.7 22772.06 69.5 270.0 18765 97.0 287.6 27897.2 Figure 1 96.6 357.1 34495.86 73.5 242.5 17823.75 Send data to Excel Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
An electric utility wishes to examine the relationship between temperature and electricity use in its service region during the summer months. The bivariate data below give the maximum temperature (denoted by x, in degrees Fahrenheit) and the electricity use (denoted b y, in thousands of kilowatt hours) for a random sample of sixteen summer days. The data are shown in the Figure 1 scatter plot. Also given are the products of the temperature values and values for electricity use for each of the sixteen days. (These products, written in the column labelled "xy," may aid in calculations.) ху, Temperature, x Electricity use, y (in degrees Fahrenheit) (in thousands of kilowatt hours) ху 82.2 254.3 20903.46 88.8 309.3 27465.84 400- 81.0 298.2 24154.2 71.9 297.4 21383.06 375- 83.4 366.5 30566.1 350- 95.4 329.0 31386.6 325- 82.8 315.0 26082 300- XX 73.1 297.7 21761.87 275- 91.7 323.7 29683.29 91.4 343.3 31377.62 250 98.4 385.7 37952.88 225- 77.8 292.7 22772.06 69.5 270.0 18765 97.0 287.6 27897.2 Figure 1 96.6 357.1 34495.86 73.5 242.5 17823.75 Send data to Excel Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
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:An electric utility wishes to examine the relationship between
temperature and electricity use in its service region during the summer
months. The bivariate data below give the maximum temperature
(denoted by x, in degrees Fahrenheit) and the electricity use (denoted by
in thousands of kilowatt hours) for a random sample of sixteen
summer days. The data are shown in the Figure 1 scatter plot. Also
given are the products of the temperature values and values for
electricity use for each of the sixteen days. (These products, written in
the column labelled "xy," may aid in calculations.)
У,
Temperature, x Electricity use, y
(in degrees
Fahrenheit)
(in thousands of
kilowatt hours)
ху
82.2
254.3
20903.46
88.8
309.3
27465.84
400-
81.0
298.2
24154.2
71.9
297.4
21383.06
375-
83.4
366.5
30566.1
350-
95.4
329.0
31386.6
325-
82.8
315.0
26082
300
73.1
297.7
21761.87
91.7
323.7
29683.29
275-
91.4
343.3
31377.62
250
98.4
385.7
37952.88
225
77.8
292.7
22772.06
69.5
270.0
18765
80
90
100
97.0
287.6
27897.2
Figure 1
96.6
357.1
34495.86
73.5
242.5
17823.75
Send data to Excel
Answer the following. Carry your intermediate computations to at least
four decimal places, and round your answer as specified below.
What is the value of the sample correlation coefficient
for these data? Round your answer to at least three
decimal places.
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