Question

Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data447.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      1.3
20      1.2
30      3.6
40      4.7
50      8
60      8.5
70      10.2
80      11.4
90      12.8
100     17.8
110     19.1
120     19.3
130     20.7
140     21.8
150     25.3
160     26.8
170     27.9
180     29.4

Answer 1

Following table shows the calculations:

	time,X	length,Y	(X-mean)^2	(Y-mean)^2	(X-mean)(Y-mean)
	10	1.3	7225	187.4161	1163.65
	20	1.2	5625	190.1641	1034.25
	30	3.6	4225	129.7321	740.35
	40	4.7	3025	105.8841	565.95
	50	8	2025	48.8601	314.55
	60	8.5	1225	42.1201	227.15
	70	10.2	625	22.9441	119.75
	80	11.4	225	12.8881	53.85
	90	12.8	25	4.7961	10.95
	100	17.8	25	7.8961	14.05
	110	19.1	225	16.8921	61.65
	120	19.3	625	18.5761	107.75
	130	20.7	1225	32.6041	199.85
	140	21.8	2025	46.3761	306.45
	150	25.3	3025	106.2961	567.05
	160	26.8	4225	139.4761	767.65
	170	27.9	5625	166.6681	968.25
	180	29.4	7225	207.6481	1224.85
Total	1710	269.8	48450	1487.2378	8448

Sample size: n= 18

Mean:

Standard deviation:

The co-variance of the data:

The correlation coefficient is

The equation of the regression line for predicting length (y) from time (x) is:

Slope of the regression equation is

Y intercept of equation is

Equation of regression line is

-------------------------

The equation of the regression line for predicting time (x) from length (y) is:

Slope of the regression equation is

X intercept of equation is

Equation of regression line is