Question

An aricle shows a soaerplet for many nations shown on he plot were approximaialy as shown in the tab 12 The soatterplot shows a srong pon tive aociation between the two arlables b. Find and interpret the predction equan Round to beo decimal places as needed barrels per The comelation is 0.87 Round to beo decimal piaces as needed) The corelation shows strong positive association befween the two varabies, with higher ail cosumgtion per person associaned wth tigher GDP ser person d. Find and interpret the residual for Nation G et 24 31 r thar would be predcd atonG has GOP that is2431 greater than would be predicsed giveni their GDP

Answer 1

X	Y	XY	X²	Y²
26	41	1066	676	1681
16	33	528	256	1089
13	31	403	169	961
1	2	2	1	4
10	11	110	100	121
9	29	261	81	841
26	41	1066	676	1681
12	29	348	144	841
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
113	217	3784	2103	7219

Sample size, n =	8
x̅ = Ʃx/n =	14.125
y̅ = Ʃy/n =	27.125
SSxx = Ʃx² - (Ʃx)²/n =	506.875
SSyy = Ʃy² - (Ʃy)²/n =	1332.875
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	718.875

Slope, b = SSxy/SSxx = 1.41825

y-intercept, a = y̅ -b* x̅ = 7.09223

b) Regression equation :

ŷ = 7.09 + 1.42x

The slope means that as the GDP per person of a country increase by one thousand dollars, the oil consumption per person tends to increase by 1.42 barrels per person.

The y-intercept is the oil consumption per person for a country with GDP per person of 0 thousand dollars. Since there are no observation with such x values, the y-intercept does not have contextual meaning.

c) Correlation:

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 0.8746

d) Predicted value for Nation G:

Predicted value of y at X =26

ŷ = 7.0922 + 1.4182 * 26 = 43.97

Residual = original- predicted = 41 - 43.97 = -2.97

Nation G has Oil consumption that is 2.97 less than would be predicted given their GDP.