Question

B) FIND THE CRITICAL VALUES
C) Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts a-c. Height (x) Interval after (y) 112 64 140 75 115 59 140 73 130 71 110 56 100 54 120 68 Click here to view a table of critical values for the correlation coefficient. a. Find the value of the linear correlation coefficient r. r= .942 (Round to three decimal places as needed.) b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using a = 0.05. The critical values are + (Round to three decimal places as needed.)

Answer 1

X	Y
112 140 115 140 130 110 100 120	64 75 59 73 71 56 54 68

X - Mx	Y - My	(X - Mx)2	(Y - My)2​​​​	(X - Mx)(Y - My)
-8.875 19.125 -5.875 19.125 9.125 -10.875 -20.875 -0.875 Mx: 120.875	-1.000 10.000 -6.000 8.000 6.000 -9.000 -11.000 3.000 My: 65.000	78.766 365.766 34.516 365.766 83.266 118.266 435.766 0.766 Sum: 1482.875	1.000 100.000 36.000 64.000 36.000 81.000 121.000 9.000 Sum: 448.000	8.875 191.250 35.250 153.000 54.750 97.875 229.625 -2.625 Sum: 768.000

Key

X: X Values
Y: Y Values
M_x: Mean of X Values
M_y: Mean of Y Values
X - M_x & Y - M_y: Deviation scores
(X - M_x)² & (Y - M_y)²: Deviation Squared
(X - M_x)(Y - M_y): Product of Deviation Scores

Result Details & Calculation

X Values
∑ = 967
Mean = 120.875
∑(X - M_x)² = SS_x = 1482.875

Y Values
∑ = 520
Mean = 65
∑(Y - M_y)² = SS_y = 448

X and Y Combined
N = 8
∑(X - M_x)(Y - M_y) = 768

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 768 / √((1482.875)(448)) = 0.9423

r= 0.942 means their is strong correlation between X and Y

b)

N=8

Significance Level:	0.05
Degrees of Freedom(N-2):	6

Critical value(two tailed) = +/- 0.707

Critical value (or tailed) = 0.621.

c)

r= 0.942 means their is strong correlation between X and Y

This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

Thank You...|||