The data show the time intervals after an eruption (to the next eruption) of a c
ID: 3129665 • Letter: T
Question
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
105 feet. Use a significance level of 0.05.
Height (ft)
115
133
137
140
99
112
108
126
Interval after (min)
75
85
94
85
66
88
68
82
Click the icon to view the critical values of the Pearson correlation coefficient r.
What is the regression equation?
Y intercept equals= 17.22 + 0.52x (this is the y intercept I concluded thus far...please double check and assist with how to get the part b answer? I am unsure about how to proceed with that part.
(Round to two decimal places as needed.)
What is the best predicted value?
Y intercept is approx how many minutes?
(Round to one decimal place as needed.)
Table below....
Critical Values of the Pearson Correlation Coefficient r
NOTE: To test
H0:
rhoequals=0
against
H1:
rhonot equals0,
reject
H0
if the absolute value of r is greater than the critical value in the table:
Critical Values of the Pearson Correlation Coefficient r
alpha =0.05
alpha =0.01
4
0.950
0.990
5
0.878
0.959
6
0.811
0.917
7
0.754
0.875
8
0.707
0.834
9
0.666
0.798
10
0.632
0.765
11
0.602
0.735
12
0.576
0.708
13
0.553
0.684
14
0.532
0.661
15
0.514
0.641
16
0.497
0.623
17
0.482
0.606
18
0.468
0.590
19
0.456
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
35
0.335
0.430
40
0.312
0.402
45
0.294
0.378
50
0.279
0.361
60
0.254
0.330
70
0.236
0.305
80
0.220
0.286
90
0.207
0.269
100
0.196
0.256
Thank you!
Explanation / Answer
What is the regression equation?
Using technology, we get
slope = 0.520893603
y-intercept = 17.21665059 [ANSWER]
********************************
What is the regression equation?
Thus, the regression line is
y^ = 0.520893603 x + 17.21665059 [ANSWER]
*****************************
What is the best predicted value?
Thus, if x = 105
Then
y^ = 71.91047895 [ANSWER]
*****************************
As alpha = 0.05, df = n - 2 = 8-2 = 6, then
rcrit = 0.811 [ANSWER, reject Ho when |r| > 0.811.]
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