Answer to Question #341545 in Statistics and Probability for John

Question

A study was conducted to determine whether there exists a relationship between the length of time (in hours) a senior high school student spends reviewing his or her lesson a week before the final examination and his or her grade in statistics and probability. Eight randomly selected senior high school students provided the following data.

x 10 12 24 20 13 13 8 22

y 80 83 94 90 85 84 80 89

Compute the Pearson’s r. Interpret the results.

PLEASE ANSWER MY QUESTION QUICKLY!!

DEADLINE : 05/20/2022 11 : 00 PM

Answer 1

Pearson`s corellation coefficient:

$r=\frac {n\sum (x_iy_i) -\sum {x_i} \sum {y_i}} {\sqrt{(n\sum {x_i^2} -(\sum {x_i})^2)*(n\sum {y_i^2} -(\sum {y_i})^2)}}$

So, we have$\sum_{i=1}^8 x_iy_i=10*80+12*83+24*94+20*90+13*85+13*84+8*80+22*89=10647$

$\sum_{i=1}^8 {x_i}=122$ , $\sum_{i=1}^8 {x_i^2}=2106$

$\sum_{i=1}^8 {y_i}=685$ , $\sum_{i=1}^8 {y_i^2}=58827$

So, $r=\frac {8*10647-122*685} {\sqrt{8*2106-122^2} *\sqrt{8*58827-685^2}}=0.972$

The range of the correlation coefficient is from -1 to 1. Our result is 0.972 or 97.2%, which means the variables have a positive correlation (it means that for every positive increase in one variable, there is a positive increase of a fixed proportion in the other).