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A teacher is assessing the correlation between the number of hours spent studying and the average score on a music test. The table shows the data:Number of hours spent studying(x)00.511.522.533.54Score on music test(y)606264666870727476Part 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 that best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)

User Ned Howley
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1 Answer

5 votes

Given:

Number of hours spent studying

(x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score on the music test

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

Required:

We need to find the function that best fits the data and slope and y-intercept of the plot.

Step-by-step explanation:

B)

Recall that a line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

Here best-fit equation is a line that passes through all given points.

Consider the line equation.


y=mx+b

where m is the slope and b is the y-intercept.

Consider the slope formula.


m=(y_2-y_1)/(x_2-x_1)

Consider points (0,60) and (1,64).


Substitute\text{ }y_2=64,y_1=60,x_2=1,\text{ and }x_1=0\text{ in the formula.}


m=(64-60)/(1-0)
m=4

Recall that the y-intercept point is the intersection point where the line meets the y-axis.

The point (0,60) is the intersection point where the line meets the y-axis.


b=60

Substitute m=4 and b =60 in the line equation.


y=4x+60

The function that best fits the data is y =4x+60.

C)

The slope of the plot indicates scores on the music test increased by 4 per one hour of studying.

The y-intercept of the plot indicates the score on the music test is 60 when they do not study.

A teacher is assessing the correlation between the number of hours spent studying-example-1
User Ajay John Alex
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