Question

Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data301.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      1.7
20      3.8
30      5.2
40      7.6
50      8.4
60      9.9
70      10.1
80      9.4
90      12.4
100     17.5
110     16.4
120     19.3
130     22.5
140     23.5
150     25.8
160     26.7
170     28.8
180     29.8

Answer 1

	time	time^2	length	length^2	time*length
	Xi	X^2	Yi	y^2	xy
	10	100	1.7	2.89	17
	20	400	3.8	14.44	76
	30	900	5.2	27.04	156
	40	1600	7.6	57.76	304
	50	2500	8.4	70.56	420
	60	3600	9.9	98.01	594
	70	4900	10.1	102.01	707
	80	6400	9.4	88.36	752
	90	8100	12.4	153.76	1116
	100	10000	17.5	306.25	1750
	110	12100	16.4	268.96	1804
	120	14400	19.3	372.49	2316
	130	16900	22.5	506.25	2925
	140	19600	23.5	552.25	3290
	150	22500	25.8	665.64	3870
	160	25600	26.7	712.89	4272
	170	28900	28.8	829.44	4896
	180	32400	29.8	888.04	5364
sum	1710	210900	278.8	5717.04	34629

formulas used:

mean = sum(Xi/n)
var = (sum(Xi^2)- n*Xbar^2)/(n-1)
sd= sqrt(var)
b1= r*Sy/Sx
bo= Ybar - b1*Xbar

calculations:

1)

time x =1710/18

95.000

2)

time s^2 = =(210900-18*95^2)/17

2850

time s = =SQRT(2850)

53.385

3)

length x= =278.8/18

15.489

4)

length s^2= =(5717.04-18*15.489^2)/17

82.27504835

length, s= =SQRT(82.27505)

9.071

5)

r= =(18*34629-1710*278.8)/SQRT((18*210900-1710^2)*(18*5717.04-278.8^2))

0.989

6)

for time = bo + b1* length

b1=

r* time s / length s

=0.989*53.385/9.071

5.821

bo=

time x - b1*length x

=95-5.821*15.489

4.839

time = 4.839 + 5.821*length

7)

for length = bo + b1* time

b1=

r* length s / time s

=0.989*53.385/9.071

0.168

bo=

length x - b1*time x

=15.489-0.168*95

-0.471

length = -0.471 + 0.168* time