Answer:
24.23 ; 13.47 ; 0.782 ; p value < 0.00001 ;7.45
Step-by-step explanation:
Given that :
ΣX = 3,416, ΣY = 1,899, SDX = 8.84, SDY = 4.70, ΣZXZY = 109.416
Sample size, N = 141
Mean of X:
£X / N = 3416 / 141 = 24.23
Mean of Y:
£Y / N = 1899 / 141 = 13.47
B.) Correlation between the 2 variables :
£ZXZY / N - 1
= 109.416 / 140
= 0.782
C.)
Level of significance and p value :
T = [Rsqrt(n-2)] ÷ sqrt(1 - R²)
T = [0.782 * sqrt(139)] ÷ sqrt(1-0.782^2)
T = 14.79
P value from Tscore calculator
Df = 141 - 2 = 139 ; α = 0.05
Pvalue = 0.00001
Pvalue < α ; Hence, a significant positive relationship exists.
To obtain regression model :
Slope = £ZXZY / SDX²
m = 109.416 / 8.84^2 = 1. 4
yintercept = meanY - slope*x
yintercept = 13.47 - 1.4*24.3
yintercept = - 20.55
Equation in slope intercept form:
y = mx + c
y = 1.4x - 20.55
For x = 20
y = 1.4(20) - 20.55
y = 7.45
