The city of Oakdale wishes to see if there is a linear relationship between the
ID: 3238512 • Letter: T
Question
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Based on the data in the table below, is there a significant linear relationship between temperature and the amount of electricity used? These data are also available in the worksheet temperature in the Excel workbook Temperature.xlsx.
Temperature.xlsx
Temperature (x)
73
78
85
98
93
81
76
105
Kilowatts (y)
680
760
910
1510
1170
837
600
1800
Temperature (x)
73
78
85
98
93
81
76
105
Kilowatts (y)
680
760
910
1510
1170
837
600
1800
Explanation / Answer
ANS= c
X Values
= 689
Mean = 86.125
(X - Mx)2 = SSx = 912.875
Y Values
= 8267
Mean = 1033.375
(Y - My)2 = SSy = 1274757.875
X and Y Combined
N = 8
(X - Mx)(Y - My) = 33461.625
R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 33461.625 / ((912.875)(1274757.875)) = 0.9809
Meta Numerics (cross-check)
r = 0.9809
r=0.981
Yes, the sample correlation coefficient is equal to 0.981, which provides evidence of a significant linear relationship.
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