The data show the time intervals after an eruption to the ne

The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 84 feet. Use a significance level of 0.05.

Height (ft),Interval after (min)
96,68
111,80
76,66
91,72
66,58
108,79
116,84
91,79

What is the regression equation?

y = _____+_____x

Solution

Linear Regression
Number of cases 8
X = 755
Y = 586
X^2 = 73351
XY = 56269
X Y = 755*586

b = ( XY - X Y / n ) / [ X^2 - (X)^2 / n]
Numerator of b = (56269) - (755)(586) / 8 = .48270.125
Denominator of b = [73351 - (755)^2 / 8] = 62084.25
b = 48270.125 / 62084.25
Regression coefficient b = 0.777
Constant = 45.59238

Equation : Y = 45.592+0.777 X