Answer:
^Y= 0.03 + 0.59Xi; r= 0.9979
Step-by-step explanation:
Hello!
Given the variables:
Y: Rainfall in cm
X: Time in hours.
The estimated regression line is:
^Y= a + bX
a= Y[bar]-bX[bar]
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{[sumX^2-\frac{(sumX)^2}{n} ]}[/tex]
∑X= 15.70; ∑X²= 53.07; ∑Y= 9.50; ∑Y²= 19.29; ∑XY= 31.98
n= 6; X[bar]= 2.62; Y[bar]= 1.58
[tex]b= \frac{31.98-\frac{15.70*9.50}{6} }{[53.07-\frac{(15.70)^2}{6} ]}= 0.59[/tex]
a= 1.58-0.59*2.62= 0.03
And the correlation coefficient:
[tex]r= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{\sqrt{[sumX^2-\frac{(sumX)^2}{n} ][sumY^2-\frac{(sumY)^2}{n} ]} } = \frac{31.98-\frac{15.70*9.50}{6} }{\sqrt{[53.07-\frac{(15.70)^2}{6} ][19.29-\frac{(9.50)^2}{6} ]} } = 0.9979[/tex]
I hope this help!
Full text
The total amounts of rainfall at various points in time during a thunderstorm are shown in the table.
Rainfall During a Thunderstorm
Time (hours)
0.4
1.1
2.9
3.2
3.7
4.4
Rainfall (cm)
0.3
0.6
1.8
2.0
2.2
2.6
According to a regression calculator, what is the equation of the line of best fit for the data?
A calculator screen. A 2-column table with 6 rows titled Data. Column 1 is labeled x with entries 0.4, 1.1, 2.9, 3.2, 3.7, 4.4. Column 2 is labeled y with entries 0.3, 0.6, 1.8, 2, 2.2, 2.6. The linear regression equation is y almost-equals 0.594 x + 0.029; r almost-equals 0.998.
y almost-equals 0.06 x + 0.03
y almost-equals 0.06 x + 0.29
y almost-equals 0.59 x + 0.03
y almost-equals 0.59 x + 0.29
