Question

A teacher is assessing the correlation between the number of hours spent studying and the average score on a music 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 music test (y) 60 62 64 66 68 70 72 74 76 Part A: Is there any correlation between the number of hours students spent studying and the score on the music 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) (10 points)

Answer 1

There is a correlation between the number of hours spent on studies and the score on music tests.

We have given that,

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 music test (y) 60 62 64 66 68 70 72 74 76

How to explain the correlation?

As we increase the 0.5 hours of studying, then the music score increases by 2. The function which best fits the data for the correlation is y=60 + 4x

The slope and y-intercept of the plot indicate that Y= score obtained in music test and number of hours spent on studying.

The slope of the above equation represents the rate of increase in music score with respect to an increase in the number of hours spent on studying.

The y-intercept gives the music score when the number of hours spent on studying is zero.

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