Question

10A) Give an example of a paired data set (with at least 5 pairs) that demonstrates a strong (but not perfect) negative linear correlation.

x	y

10B) Give a real life example of two variables that are likely to be positively correlated. Specifically explain why you believe your chosen two variables are positively correlated.

10C) Suppose some researchers studied children in high schools and found a strong positive linear correlation between the availability of vending machines and obesity.   From this correlation, can we determine that having vending machines in high schools causes children to be obese?   Explain your answer.

Answer 1

Answer:

10)a)

Consider the values,

x          y

5          100

10        70

15        60

20        40

30        20

For this. (X- x bar x-xbar 16 16 y bar 58 58 y-ybar 42 | 12 16 (x- xbar)^2 121 36 1 16 196 370 xbar)(y- ybar) -462 -72 -2 -72 -532 (v- ybar)^2 1764 144 4 324 1444 3680 58 58 58 16 16 14 -38 -1140 sum/total=80/5=16 sum total=290/5=58 r=-1140/sqrt[(370 (3680)] r=-0.9769 Here, Strong negative relationship exists between x and y i.e., if x increases then y decreases.

10)b)

In everyday life, two variables which can be stated as positively correlated mainly include the support from co-workers and self esteem. This can be said as positively correlated with work and everyday life as it is directly proportional to the increase in the performance of the person.