the second and third picture is the table. The data show the time intervals afte

Question

the second and third picture is the table.

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 70 feet. Use a significance level of 0.05. Height (t) Interval after (min) Click the icon to view the critical values of the Pearson correlation coefficient r 1 73 111 100 99 120 73 77 112 67 84 67 77 84 58 69 70 What is the regression equation? x(Round to two decimal places as needed) What is the best predicted time for the interval after an eruption that is 70 feet high? ys minutes (Round to one decimal place as needed.)

Explanation / Answer

Line of Regression Y on X i.e Y = bo + b1 X

calculation procedure for regression

mean of X = X / n = 95.625

mean of Y = Y / n = 72

(Xi - Mean)^2 = 2499.87

(Yi - Mean)^2 = 572

(Xi-Mean)*(Yi-Mean) = 925.01

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 925.01 / 2499.87

= 0.37

bo = Y / n - b1 * X / n

bo = 72 - 0.37*95.625 = 36.62

value of regression equation is, Y = bo + b1 X

Y'=36.62+0.37* X

calculation procedure for correlation

sum of (x) = x = 765

sum of (y) = y = 576

sum of (x^2)= x^2 = 75653

sum of (y^2)= y^2 = 42044

sum of (x*y)= x*y = 56005

to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)

covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1

= 56005 - [ 8 * (765/8) * (576/8) ]/8- 1

= 115.625

and now to calculate r( x,y) = 115.625/ (SQRT(1/8*56005-(1/8*765)^2) ) * ( SQRT(1/8*56005-(1/8*576)^2)

=115.625 / (17.677*8.456)

=0.774

value of correlation is =0.774

coeffcient of determination = r^2 = 0.598

properties of correlation

1. If r = 1 Corrlation is called Perfect Positive Corrlelation

2. If r = -1 Correlation is called Perfect Negative Correlation

3. If r = 0 Correlation is called Zero Correlation

& with above we conclude that correlation ( r ) is = 0.7735> 0 ,perfect positive correlation

Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 67 511.89 25 113.13 84 236.39 144 184.5 67 19.14 25 -21.88 77 11.39 25 16.88 84 594.14 144 292.5 58 511.89 196 316.75 69 346.89 9 55.88 70 268.14 4 -32.75

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