Question

A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table 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 that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

1. linhdan
The number of hours students spent studying and the score on the science test are in linear correlation , a function that best fits the data is y = 4x + 60 and the slope and y-intercept of the plot indicate that y -intercept is the lowest score with no time spent studying

### Linear Correlation

Linear Correlation is a measure of the degree to which two variables vary together, or a measure of the intensity of the association between two variables.

### What are the steps to solve this problem?

The steps are as follow:
• We can see there is a relation between x and y values that for every step change of x = 0.5, every step change of y = 2
• So the relationship is linear
• By using to pairs of points to get the slope and y-intercept (0, 60) and (1, 64)
• And Calculating the slope:
m = (64 – 60)/(1 – 0) = 4/1 = 4
• y – intercept is 60 as per point (0, 60)
• So the function is y = 4x + 60
• The slope and y-intercept of the plot indicate lowest score with no time spent studying
So, the number of hours students spent studying and the score on the science test are in linear correlation , a function that best fits the data is y = 4x + 60 and the slope and y-intercept of the plot indicate that y -intercept is the lowest score with no time spent studying
#SPJ2

2. Answer: From the table we see there is a relation between x and y values
Every step change of x = 0.5, every step change of y = 2
This relation is linear. The formula for linear function is:
y = mx + b
Using to pairs of points to get the slope and y-intercept
(0, 60) and (1, 64)
Calculating the slope:
m = (64 – 60)/(1 – 0) = 4/1 = 4
y – intercept is 60 as per point (0, 60)
So the function is
y = 4x + 60
Part A
Yes. Described above
Part B
y = 4x + 60
Part C
Slope is the steepness of the line.
y -intercept is the lowest score with no time spent studying
HOPE I HELPED ! Have a great day 🙂