Question

You go to a carnival and a sideshow performer wants to bet you $100 that he can guess your exact weight just from knowing your height. You watch him for a few moments predicting people's weights and get the following observations. (Assume a linear relationship).

Height (in) Weight(lbs)
60.0 99
62.0 107
63.0 111
66.5 125
73.5 153
84.0 195
The performer is predicting
Height from weight
Weight from height
Unable to determine
The ∑ X is
790
28,293.5
11,0,630
55,505
409
The ∑ Y is
790
28,293.5
11,0,630
55,505
409
The ∑ X Y is
790
28,293.5
11,0,630
55,505
409
Should you take his bet?
Yes
No
Unable to determine

Answer 1

Weight from height ;

409 ;

790 ;

55,505

Yes

Explanation:

Height, X :

ΣX = (60+62+63+66.5+73.5+84) = 409

Weight, Y :

ΣY = (99 + 107 + 111 + 125 + 153 + 195) = 790

Height * weight = ΣXY

(60*99 +62*107 +63*111 +66.5*125 +73.5*153 +84*195) = 55,505

To know If to take the bet, we calculate the strength of the relationship :

Correlation Coefficient :

Using calculator :

The correlation Coefficient = 1 ; meaning that there is a perfect relationship between height and weight. Hence, take the bet.