Question 823781: The amount of rainfall today is crucial in analyzing the future amount. The data was gathered to estimate given the time of the day. What is the regression equation of this data?
Forecast Actual
9:00 AM 3.6 0
9:15 AM 2 1.2
9:30 AM 1.1 1.2
9:45 AM 1.3 1.3
10:00 AM 1.8 1.4
10:15 AM 2.1 1.4
10:30 AM 3.2 2
10:45 AM 2.7 2.1
11:00 AM 2.5 2.5
11:15 AM 3.5 2.9
11:30 AM 3.9 4
11:45 AM 3.5 4.9
12:00 PM 6.5 6.2
12:15 PM 7.3 6.6
12:30 PM 6.4 7.8
Coefficient(b1) 1.062436733 -0.607283204 Intercept Coefficient(b0)
Standard Error 0.166032221 0.646602602 Intercept Standard Error
R Square 0.759022455 1.189992822 Standard Error
F 40.94693519 13 Residual df
Regression MS 57.98425541 18.40907792 Residual MS
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
the given ACTUAL data samples:
9:00 0.0
9:15 1.2
9:30 1.2
9:45 1.3
10:00 1.4
10:15 1.4
10:30 2.0
10:45 2.1
11:00 2.5
11:15 2.9
11:30 4.0
11:45 4.9
12:00 6.2
12:15 6.6
12:30 7.8
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convert time to minutes since midnight:
540 0.0
555 1.2
570 1.2
585 1.3
600 1.4
615 1.4
630 2.0
645 2.1
660 2.5
675 2.9
690 4.0
705 4.9
720 6.2
735 6.6
750 7.8
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perform a linear regression over the sample data:
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copy and paste the above sample data in to this linear regression solver:
https://sooeet.com/math/linear-regression.php
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alpha (y-intercept) = -18.1134524
beta (slope) = 0.0327857143
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answer:
slope-intercept form of the regression line:
y(x) = (0.0327857143)x - 18.1134524
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NOTE:
x units are minutes past midnight, rather than clock time
y units are the rainfall measurement units given in the sample data (for example mm, cm, etc.)
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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