Question

Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data79.dat. Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Use the same five numbers to find the equation of the regression line for predicting the time an icicle has been growing from its length. (Round your answers to three decimal places.)

times x =

times s =

lengths x =

lengths s =

r =

time = + length

length = time  

time length
10   .8
20   3
30   5.5
40   4.9
50   9.4
60   8.6
70   9.5
80   15
90   15.2
100   15.6
110   17.2
120   19.9
130   21.6
140   22.7
150   26
160   26.3
170   27.4
180   31.1

Answer 1

Solution:

Here, we have to find the regression equation for the prediction of the length based on time. Also, we have to find the regression equation for the prediction of the time based on length.

Let us first find the regression equation for the prediction of the length based on time.

Here, we have x = time and y = length

From given data, we have

Xbar = 95

Ybar = 15.53889

Sx = 53.38539

Sy = 9.168369

Correlation coefficient = r = 0.993478

(Sample means, standard deviations, correlation coefficient are calculated by using excel)

Formulas for finding the regression coefficients are given as below:

b = r*Sy/Sx

a = Ybar – b*Xbar

b = 0.993478*9.168369/53.38539

b = 0.170619

a = 15.53889 - 0.170619*95

a = -0.66991

Regression equation is given as below:

y = a + b*x

y = -0.66991 + 0.170619*x

y = -0.670 + 0.171*x

Now, we have to find the regression equation for the prediction of the time based on length.

Here, we have x = length and y = time

From given data, we have

Ybar = 95

Xbar = 15.53889

Sy = 53.38539

Sx = 9.168369

Correlation coefficient = r = 0.993478

b = r*Sy/Sx

a = Ybar – b*Xbar

b = 0.993478*53.38539/9.168369

b = 5.784803

a = 95 - 5.784803*15.53889

a = 5.110583

Regression equation is given as below:

y = a + b*x

y = 5.110583 + 5.784803*x

y = 5.111 + 5.785*x