Ateacher is assessing the correlation between the number of hours spent studying and the average score on a science test. the table below shows the data:

number of hours spent studying
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4
score on science test
(y) 57 62 67 72 77 82 87 92 97

part a: is there any correlation between the number of hours students spent studying and the score on the science test? justify your answer. (4 points)

part b: write a function which best fits the data. (3 points)

part c: what does the slope and y-intercept of the plot indicate? (3 points)

a. as we can see, an increase in 0.5 hours of studying (x) leads to an increase in 5 units of score (y). therefore we can say that there is indeed a correlation between the number of hours students spent studying and the score on the science test.

b. the function is a straight-line with a standard equation of y = m x + b

calculating for m:

m = y2 – y1 / (x2 – x1)

m = (62 – 57) / (0.5 – 0)

m = 10

finding for b (y – intercept): b is the value of y when x = 0, therefore from the given data, b = 57

the whole equation becomes:

y = 10 x + 57

c. the slope m=y/x=10 indicates that for every 1 hour spent on studying, 10 units of score is added. the intercept shows that when a student do not study, he gets a score of 57.